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MAT 540 Final Exam (20 Sets)
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This Tutorial contains 20 Sets of Final Exam (800 Questions/Answers)
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MAT 540 Midterm Exam (5 Sets)
This Tutorial contains 5 Sets of Midterm Exam
MAT 540 Midterm Exam Set 1
Question 1 Deterministic techniques assume that no uncertainty exists
in model parameters.

Question 2 A joint probability is the probability that two or more
events that are mutually exclusive can occur simultaneously.
Question 3 A continuous random variable may assume only integer
values within a given interval.
Question 4 A decision tree is a diagram consisting of circles decision
nodes, square probability nodes, and branches.
Question 5 Simulation results will always equal analytical results if 30
trials of the simulation have been conducted.
Question 6 Excel can only be used to simulate systems that can be
represented by continuous random variables.
Question 7 Data cannot exhibit both trend and cyclical patterns.
Question 8 The Delphi develops a consensus forecast about what will
occur in the future.
Question 9 In Bayesian analysis, additional information is used to alter
the __________ probability of the occurrence of an event.
Question 10 __________ is a measure of dispersion of random
variable values about the expected value.
Question 11 The __________ is the maximum amount a decision
maker would pay for additional information.
Question 12 Developing the cumulative probability distribution helps
to determine
Question 13 A seed value is a(n)

Question 14 Pseudorandom numbers exhibit __________ in order to
be considered truly random.
Question 15 Consider the following frequency of demand:
If the simulation begins with 0.8102, the simulated value for demand
would be
Question 16 __________ is a linear regression model relating demand
to time.
Question 17 worth 2 points, 1 hour time limit (chapters 1,ue units
EXCEPT:The U.S. Department of Agriculture estimates that the yearly
yield of limes per acre is distributed as follows:
Yield, bushels per acre Probability
350 .10
400 .18
450 .50
500 .22
The estimated average price per bushel is $16.80.
What is the expected yield of the crop?
Question 18 __________ methods are the most common type of
forecasting method for the long-term strategic planning process.
Question 19 In exponential smoothing, the closer alpha is to
__________, the greater the reaction to the most recent demand.

Question 20 Given the following data on the number of pints of ice
cream sold at a local ice cream store for a 6-period time frame:
If the forecast for period 5 is equal to 275, use exponential smoothing
with α = .40 to compute a forecast for period 7.
Question 21
Question 22 Coefficient of determination is the percentage of the
variation in the __________ variable that results from the __________
variable.
Question 23 Which of the following possible values of alpha would
cause exponential smoothing to respond the most slowly to sudden
changes in forecast errors?
Question 24 Consider the following demand and forecast.
Period Demand Forecast
1 7 10
2 12 15
3 18 20
4 22
If MAD = 2, what is the forecast for period 4?
Question 25 An automotive center keeps tracks of customer complaints
received each week. The probability distribution for complaints can be
represented as a table or a graph, both shown below. The random
variable xi represents the number of complaints, and p(xi) is the
probability of receiving xi complaints.
xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07

What is the average number of complaints received per week? Round
your answer to two places after the decimal.
Question 26 An online sweepstakes has the following payoffs and
probabilities. Each person is limited to one entry.
The probability of winning at least $1,000.00 is ________.
Question 27 A fair die is rolled 8 times. What is the probability that an
even number (2,4, 6) will occur between 2 and 4 times? Round your
answer to four places after the decimal.
Question 28 A life insurance company wants to estimate their annual
payouts. Assume that the probability distribution of the lifetimes of the
participants is approximately a normal distribution with a mean of 68
years and a standard deviation of 4 years. What proportion of the plan
recipients would receive payments beyond age 75? Round your answer
to four places after the decimal.
Question 29 The local operations manager for the IRS must decide
whether to hire 1, 2, or 3 temporary workers. He estimates that net
revenues will vary with how well taxpayers comply with the new tax
code. The following payoff table is given in thousands of dollars (e.g. 50
= $50,000).
If he uses the maximin criterion, how many new workers will he hire?
Question 30 An investor is considering 4 different opportunities, A, B,
C, or D. The payoff for each opportunity will depend on the economic
conditions, represented in the payoff table below.

Economic Condition
Poor Average Good Excellent
Investment (S1) (S2) (S3) (S4)
A 50 75 20 30
B 80 15 40 50
C -100 300 -50 10
D 25 25 25 25
If the probabilities of each economic condition are 0.5, 0.1, 0.35, and
0.05 respectively, what is the highest expected payoff?
Question 31 A normal distribution has a mean of 500 and a standard
deviation of 50. A manager wants to simulate one value from this
distribution, and has drawn the number 1.4 randomly. What is the
simulated value?
Question 32 Consider the following annual sales data for 2001-2008.
Calculate the correlation coefficient . Use four significant digits after the
decimal.
Question 33 The following data summarizes the historical demand for a
product.
Use exponential smoothing with α = .2 and the smoothed forecast for
July is 32. Determine the smoothed forecast for August.
Question 34 Robert wants to know if there is a relation between money
spent on gambling and winnings.

What is the coefficient of determination? Note: please report your
answer with 2 places after the decimal point.
Compute a 3-period moving average for period 6. Use two places after
the decimal.
Question 36 Given the following data, compute the MAD for the
forecast.
the decimal.
Question 38 The following sales data are available for 2003-2008 :
Calculate the absolute value of the average error. Use three significant
digits after the decimal.
Question 39 The following data summarizes the historical demand for
a product
If the forecasted demand for June, July and August is 32, 38 and 42,
respectively, what is MAPD? Write your answer in decimal form and
not in percentages. For example, 15% should be written as 0.15. Use
three significant digits after the decimal.

Question 40 This is the data from the last 4 weeks:
Use the equation of the regression line to forecast the increased sales for
when the number of ads is 10.
Question 2 A joint probability is the probability that two or more events
that are mutually exclusive can occur simultaneously.
Question 3 An inspector correctly identifies defective products 90% of
the time. For the next 10 products, the probability that he makes fewer
than 2 incorrect inspections is 0.736.
Question 5 Starting conditions have no impact on the validity of a
simulation model.
Question 8 Qualitative methods are the least common type of

Question 9 __________ is a measure of dispersion of random variable
values about the expected value.
Question 11 The __________ is the expected value of the regret for
each decision.
Question 12 Developing the cumulative probability distribution helps to
determine
Question 14 In the Monte Carlo process, values for a random variable
are generated by __________ a probability distribution.
Question 15 Two hundred simulation runs were completed using the
probability of a machine breakdown from the table below. The average
number of breakdowns from the simulation trials was 1.93 with a
standard deviation of 0.20.
Question 17 __________ is absolute error as a percentage of demand.
Question 18 __________ is a category of statistical techniques that uses
historical data to predict future behavior.

Question 19 Worth 2 points, 1 hour time limit (chapters 1,ue units
to time.
Question 23 __________ is the difference between the forecast and
actual demand.
Question 25 A loaf of bread is normally distributed with a mean of 22
oz and a standard deviation of 0.5 oz. What is the probability that a loaf
is larger than 21 oz? Round your answer to four places after the decimal.
Question 27 A fair die is rolled 8 times. What is the probability that an
even number (2,4, 6) will occur between 2 and 4 times? Round your
answer to four places after the decimal.

code. The following payoff table is given in thousands of dollars (e.g.
50 = $50,000).
If he thinks the chances of low, medium, and high compliance are 20%,
30%, and 50% respectively, what is the expected value of perfect
information? Note: Please express your answer as a whole number in
thousands of dollars (e.g. 50 = $50,000). Round to the nearest whole
number, if necessary.
Question 31 Given the following random number ranges and the
following random number sequence: 62, 13, 25, 40, 86, 93, determine
the average demand for the following distribution of demand.
product

product.
Use exponential smoothing with α = .2 and the smoothed forecast for
July is 32. Determine the smoothed forecast for August.
Question 34 Daily highs in Sacramento for the past week (from least to
most recent) were: 95, 102, 101, 96, 95, 90 and 92. Develop a forecast
for today using a 2 day moving average.
Question 36 This is the data from the last 4 weeks:
for today using a weighted moving average, with weights of .6, .3 and .1,
where the highest weights are applied to the most recent data.
forecast.

Year Demand Forecast
the decimal.
the decimal.

Question 6 A table of random numbers must be normally distributed
and efficiently generated.
Question 11 The __________ is the maximum amount a decision
maker would pay for additional information.
Question 12 Pseudorandom numbers exhibit __________ in order to
be considered truly random.
to determine
would be
Question 15 Random numbers generated by a __________ process
instead of a __________ process are pseudorandom numbers.

Question 16 __________ is a category of statistical techniques that
uses historical data to predict future behavior.
Question 18 Consider the following graph of sales.
Which of the following characteristics is exhibited by the data?
Question 19 Consider the following demand and forecast.
Period Demand Forecast
1 7 10
2 12 15
3 18 20
4 22
If MAD = 2, what is the forecast for period 4?

What is the expected value at node 4? Round your answer to the nearest
whole number. Do not include the dollar sign “$” in your answer.
Question 31 A normal distribution has a mean of 500 and a standard
deviation of
the decimal.
Question 33 The following sales data are available for 2003-2008.
Determine a 4-year weighted moving average forecast for 2009, where
weights are W1 = 0.1, W2 = 0.2, W3 = 0.2 and W4 = 0.5.
Question 34 The following data summarizes the historical demand for
a product

decimal.
for today using a weighted moving average, with weights of .6, .3 and .1,
where the highest weights are applied to the most recent data.
the decimal.
forecast.

Question 5 Simulation results will always equal analytical results if 30
trials of the simulation have been conducted.
Question 6 A table of random numbers must be normally distributed
and efficiently generated.
Question 9 Assume that it takes a college student an average of 5
minutes to find a parking spot in the main parking lot. Assume also that
this time is normally distributed with a standard deviation of 2 minutes.
What time is exceeded by approximately 75% of the college students
when trying to find a parking spot in the main parking lot?
Question 10 In Bayesian analysis, additional information is used to
alter the __________ probability of the occurrence of an event.
each decision.

would be
Question 13 Pseudorandom numbers exhibit __________ in order to be
considered truly random.
to determine
Question 16 __________ is a measure of the strength of the
relationship between independent and dependent variables.
to time.
Question 18 Coefficient of determination is the percentage of the
variation in the __________ variable that results from the __________
variable.
Question 19 __________ is the difference between the forecast and
actual demand.

Question 22 worth 2 points, 1 hour time limit (chapters 1,ue units
Yield, bushels per acre Probability
350 .10
400 .18
450 .50
500 .22
Question 26 A loaf of bread is normally distributed with a mean of 22
oz and a standard deviation of 0.5 oz. What is the probability that a loaf
is larger than 21 oz? Round your answer to four places after the decimal.
Question 27 The drying rate in an industrial process is dependent on
many factors and varies according to the following distribution.
Compute the mean drying time. Use two places after the decimal.

code.
If he is conservative, how many new workers will he hire?
• Question 31 Consider the following distribution and random
numbers:
If a simulation begins with the first random number, what would the first
simulation value would be __________.
• Question 32 This is the data from the last 4 weeks:

the decimal.
forecast.
decimal.
What is the coefficient of determination? Use two significant places
after the decimal.
product
Question 38 The following sales data are available for 2003-2008.
Determine a 4-year weighted moving average forecast for 2009, where
weights are W1 = 0.1, W2 = 0.2, W3 = 0.2 and W4 = 0.5.

Question 40 The following sales data are available for 2003-2008 :
Calculate the absolute value of the average error. Use three significant
digits after the decimal.
Question 6 Starting conditions have no impact on the validity of a
simulation model.
Question 7 Qualitative methods are the least common type of

What time is exceeded by approximately 75% of the college students
when trying to find a parking spot in the main parking lot?
each decision.
Question 12 Consider the following frequency of demand: If the
simulation begins with 0.8102, the simulated value for demand would be
Question 13 Random numbers generated by a __________ process
instead of a __________ process are pseudorandom numbers.
Question 14 Two hundred simulation runs were completed using the
probability of a machine breakdown from the table below. The average
number of breakdowns from the simulation trials was 1.93 with a
standard deviation of 0.20.
No. of breakdowns per week Probability Cumulative probability
What is the probability of 2 or fewer breakdowns?
Question 15 Pseudorandom numbers exhibit __________ in order to be
considered truly random.

to time.
Question 19 rob 14, and 15)estion worth 2 points, 1 hour time limit
(chapters 1,ue units EXCEPT:The U.S. Department of Agriculture
estimates that the yearly yield of limes per acre is distributed as follows:
Question 21 __________ is absolute error as a percentage of demand.
Question 22 Consider the following graph of sales. Which of the
following characteristics is exhibited by the data?
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MAT 540 Week 1 Discussion Class
Introductions

"Class Introductions" Please respond to the following:
• Please introduce yourself, including your educational and career goals,
as well as some personal information about yourself. In your
introduction, please draw from your own experience (or use a search
engine) to give an example of how probability is used in your chosen
profession. If you get your information from an online or other resource,
be sure to cite the source of the information
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MAT 540 Week 1 Homework Chapter 1 and
Chapter 11 (Solutions 100% Correct)
MAT 540 Week 1 Homework Chapter 1
1. The Retread Tire Company recaps tires. The fixed annual cost of the
recapping operation is
$65,000. The variable cost of recapping a tire is $7.5. The company
charges$25 to recap a tire.

a. For an annual volume of 15, 000 tire, determine the total cost, total
revenue, and profit.
b. Determine the annual break-even volume for the Retread Tire
Company operation.
2. Evergreen Fertilizer Company produces fertilizer. The company’s
fixed monthly cost is $25,000,
and its variable cost per pound of fertilizer is $0.20. Evergreen sells the
fertilizer for $0.45 per
pound. Determine the monthly break-even volume for the company.
3. If Evergreen Fertilizer Company in problem 2 changes the price of its
fertilizer from $0.45 per
pound to $0.55 per pound, what effect will the change have on the
break-even volume?
4. If Evergreen Fertilizer Company increases its advertising expenditure
by $10,000 per year, what
effect will the increase have on the break-even volume computed in
problem 2?
5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside
Tech’s football stadium
during home games. There are 6 home games scheduled for the
upcoming season. She must pay the
Tech athletic department a vendor’s fee of $3,000 for the season. Her
stand and other equipment
will cost her $3,500 for the season. She estimates that each hot dog she
sells will cost her $0.40. she
has talked to friends at other universities who sell hot dogs at games.
Based on their information

and the athletic department’s forecast that each game will sell out, she
anticipates that she will sell
approximately 1,500 hot dogs during each game.
a. What price should she charge for a hot dog in order to break even?
b. What factors might occur during the season that would alter the
volume sold and thus the
break-even price Annie might charge?
6. The college of business at Kerouac University is planning to begin an
online MBA program. The
initial start-up cost for computing equipment, facilities, course
development and staff recruitment
and development is $400,000. The college plans to charge tuition of
$20,000 per student per year.
However, the university administration will charge the college $10,000
per student for the first 100
students enrolled each year for administrative costs and its share of the
tuition payments.
a. How many students does the college need to enroll in the first year to
break-even?
b. If the college can enroll 80 students the first year, how much profit
will it make?
MAT540 Homework
c. The college believes it can increase tuition to $25,000, but doing so
would reduce enrollment to
50. Should the college consider doing this?
7. The following probabilities for grades in management science have
been determined based on past

records:
Grade Probability
A 0.1
B 0.2
C 0.4
D 0.2
F 0.10
1.00
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0,
and so on. Determine the
expected grade and variance for the course.
8. An investment firm is considering two alternative investments, A and
B, under two possible future
sets of economic conditions good and poor. There is a .60 probability of
good economic conditions
occurring and a .40 probability of poor economic conditions occurring.
The expected gains and
losses under each economic type of conditions are shown in the
following table:
Investment
Economic Conditions
Good Poor
A $380,000 -$100,000
B $130,000 $85,000
Using the expected value of each investment alternative, determine
which should be selected.
9. The weight of the bags of fertilizer is normally distributed, with a
mean of 45 pounds and a
standard deviation of 5 pounds. What is the probability that a bag of
fertilizer will weigh between
38 and 50 pounds

10. The polo Development Firm is building a shopping center. It has
informed renters that their rental
spaces will be ready for occupancy in 18 months. If the expected time
until the shopping center is
completed is estimated to be 15 months, with a standard deviation of 5
months, what is the
probability that the renters will not be able to occupy in 18 months?
11. The manager of the local National Video Store sells videocassette
recorders at discount prices. If
the store does not have a video recorder in stock when a customer wants
to buy one, it will lose the
sale because the customer will purchase a recorder from one of the many
local competitors. The
problem is that the cost of renting warehouse space to keep enough
recorders in inventory to meet
all demand is excessively high. The manager has determined that if 85%
of customer demand for
recorders can be met, then the combined cost of lost sales and inventory
will be minimized. The
manager has estimated that monthly demand for recorders is normally
distributed, with a mean of
175 recorders and a standard deviation of 55. Determine the number of
recorders the manager
should order each month to meet 85% of customer demand.
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MAT 540 Week 1-10 All Homework

MAT 540 Week 1 Homework Chapter 1 and Chapter 11
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MAT 540 Week 1-11 All Discussion Question

MAT 540 Week 1 Discussion Class Introductions
MAT 540 Week 2 Discussion Expected value of perfect information
MAT 540 Week 3 Discussion Simulation
MAT 540 Week 4 Discussion Forecasting Methods
MAT 540 Week 5 Discussion Reflection
MAT 540 Week 6 Discussion LP Models
MAT 540 Week 7 Discussion sensitivity analysis
MAT 540 Week 8 Discussion Practice setting up linear programming
models for business applications
MAT 540 Week 9 Discussion Application of Integer Programming
MAT 540 Week 10 Discussion Transshipment problems
MAT 540 Week 11 Discussion Reflection to Date
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MAT 540 Week 1-11 All Homework, DQs,
Midterm (5 Set) , Final Exam (20 Set)

MAT 540 Midterm Exam (5 Sets)
MAT 540 Final Exam (20 Sets)
MAT 540 Week 1 Homework Chapter 1 and Chapter 11
MAT 540 Week 1 Discussion Class Introductions
MAT 540 Week 2 Discussion Expected value of perfect information

MAT 540 Week 4 Discussion Forecasting Methods
MAT 540 Week 8 Discussion Practice setting up linear programming
models for business applications
MAT 540 Week 9 Discussion Application of Integer Programming
MAT 540 Week 10 Discussion Transshipment problems
MAT 540 Week 11 Discussion Reflection to Date
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MAT 540 Week 2 Discussion Expected value of
perfect information
In your own words, explain how to obtain the “expected value of perfect
information” for any payoff table, which has probabilities associated

with each state of nature. Then, provide an example, drawing from any
of the payoff tables in Problems 1-17 in the back of Chapter 12. If no
probabilities are given for the states of nature, then assume equal
likelihood.
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MAT540
Week 2 Homework
Chapter 12
1. A local real estate investor in Orlando is considering three
alternative investments; a motel, a restaurant, or a theater. Profits from
the motel or restaurant will be affected by the availability of gasoline
and the number of tourists; profits from the theater will be relatively
stable under any conditions. The following payoff table shows the profit
or loss that could result from each investment:
Determine the best investment, using the following decision criteria.
a. Maximax

b. Maximin
c. Minimax regret
d. Hurwicz (α = 0.4)
e. Equal likelihood
2. A concessions manager at the Tech versus A&M football game
must decide whether to have the vendors sell sun visors or umbrellas.
There is a 35% chance of rain, a 25% chance of overcast skies, and a
40% chance of sunshine, according to the weather forecast in college
junction, where the game is to be held. The manager estimates that the
following profits will result from each decision, given each set of
weather conditions:
a. Compute the expected value for each decision and select the best
one.
b. Develop the opportunity loss table and compute the expected
opportunity loss for each decision.
3. Place-Plus, a real estate development firm, is considering several
alternative development projects. These include building and leasing an
office park, purchasing a parcel of land and building an office building
to rent, buying and leasing a warehouse, building a strip mall, and
selling condominiums. The financial success of these projects depends
on interest rate movement in the next 5 years. The various development
projects and their 5- year financial return (in $1,000,000s) given that
interest rates will decline, remain stable, or increase, are in the following
payoff table. Place-Plus real estate development firm has hired an
economist to assign a probability to each direction interest rates may
take over the next 5 years. The economist has determined that there is a

0.45 probability that interest rates will decline, a 0.35 probability that
rates will remain stable, and a
0.2 probability that rates will increase.
a. Using expected value, determine the best project.
b. Determine the expected value of perfect information.
4. The director of career advising at Orange Community College
wants to use decision analysis to provide information to help students
decide which 2-year degree program they should pursue. The director
has set up the following payoff table for six of the most popular and
successful degree programs at OCC that shows the estimated 5-Year
gross income ($) from each degree for four future economic conditions:
Determine the best degree program in terms of projected income, using
the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz (α=0.4)
5. Construct a decision tree for the following decision situation and
indicate the best decision.
Fenton and Farrah Friendly, husband-and-wife car dealers, are soon
going to open a new dealership. They have three offers: from a foreign

compact car company, from a U.S. producer of full-sized cars, and from
a truck company. The success of each type of dealership will depend on
how much gasoline is going to be available during the next few years.
The profit from each type of dealership, given the availability of gas, is
shown in the following payoff table:
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MAT 540 Week 2 Quiz 1 (3 Sets)
MAT 540 Week 2 Quiz 1 Set 1 QUESTIONS
Question 1: Parameters are known, constant values that are usually
coefficients of variables in equations.
Question 2: If variable costs increase, but price and fixed costs are held
constant, the break even point will decrease.
Question 3: Probabilistic techniques assume that no uncertainty exists
Question 4: Fixed cost is the difference between total cost and total
variable cost.
Question 5: A binomial probability distribution indicates the probability
of r successes in n trials.
Question 6: The events in an experiment are mutually exclusive if only
one can occur at a time.
Question 7: If events A and B are independent, then P(A|B) = P(B|A).

Question 8: If fixed costs increase, but variable cost and price remain
the same, the break even point
Question 9: If the price increases but fixed and variable costs do not
change, the break even point
Question 10: A bed and breakfast breaks even every month if they book
30 rooms over the course of a month. Their fixed cost is $4200 per
month and the revenue they receive from each booked room is $180.
What their variable cost per occupied room?
Question 11: EKA manufacturing company produces Part # 2206 for
the aerospace industry. Each unit of part # 2206 is sold for $15. The unit
production cost of part # 2206 is $3. The fixed monthly cost of operating
the production facility is $3000. How many units of part # 2206 have to
be sold in a month to break-even?
Question 12: In a binomial distribution, for each of n trials, the event
Question 13: The expected value of the standard normal distribution is
equal to
Question 14: The area under the normal curve represents probability,
and the total area under the curve sums to
Question 15: Administrators at a university are planning to offer a
summer seminar. The costs of reserving a room, hiring an instructor, and
bringing in the equipment amount to $3000.
Suppose that it costs $25 per student for the administrators to provide
the course materials. If we know that 20 people will attend, what price
should be charged per person to break even? Note: please report the
result as a whole number, rounding if necessary and omitting the
decimal point.
Question 16: A production process requires a fixed cost of $50,000. The
variable cost per unit is $25 and the revenue per unit is projected to be
$45. Find the break-even point.
Question 17: Administrators at a university will charge students $158 to
attend a seminar. It costs $2160 to reserve a room, hire an instructor, and
bring in the equipment. Assume it costs $50 per student for the
administrators to provide the course materials. How many students
would have to register for the seminar for the university to break even?

Note: please report the result as a whole number, omitting the decimal
point.
Question 18: Wei is considering pursuing an MS in Information
Systems degree. She has applied to two different universities. The
acceptance rate for applicants with similar qualifications is 20% for
University X and 45% for University Y. What is the probability that Wei
will be accepted by at least one of the two universities? {Express your
answer as a percent. Round (if necessary) to the nearest whole percent
and omit the decimal. For instance, 20.1% would be written as 20}
Question 19: An inspector correctly identifies defective products 90%
of the time. For the next 10 products, what is the probability that he
makes fewer than 2 incorrect inspections?Note: Please report your
answer with two places to the right of the decimal, rounding if
appropriate.
Question 20: An automotive center keeps tracks of customer complaints
represented as a table (shown below). The random variable xi represents
the number of complaints, and p(xi) is the probability of receiving xi
complaints.
xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07
What is the average number of complaints received per week? Note:
Please report your answer with two places to the right of the decimal,
rounding if appropriate.
Question 1 Probabilistic techniques assume that no uncertainty exists in
model parameters.
Question 2 Fixed cost is the difference between total cost and total
variable cost.
Question 3 If variable costs increase, but price and fixed costs are held

Question 4 Parameters are known, constant values that are usually
Question 5 If events A and B are independent, then P(A|B) = P(B|A).
Question 7 The events in an experiment are mutually exclusive if only
Question 8 If fixed costs increase, but variable cost and price remain the
same, the break even point
Question 9 If the price increases but fixed and variable costs do not
Question 10 The indicator that results in total revenues being equal to
total cost is called the
Question 11 A model is a functional relationship that includes:
Question 12 In a binomial distribution, for each of n trials, the event
Question 13 The area under the normal curve represents probability, and
the total area under the curve sums to
Question 14 The expected value of the standard normal distribution is
equal to
Question 15 Administrators at a university will charge students $158 to
attend a seminar. It costs $2160 to reserve a room, hire an instructor, and
bring in the equipment. Assume it costs $50 per student for the
administrators to provide the course materials. How many students
would have to register for the seminar for the university to break even?
Note: please report the result as a whole number, omitting the decimal
point.
Question 16 A production run of toothpaste requires a fixed cost of
$100,000. The variable cost per unit is $3.00. If 50,000 units of
toothpaste will be sold during the next month, what sale price must be
chosen in order to break even at the end of the month? Note: please
report the result as a whole number, rounding if necessary and omitting
the decimal point.
Question 17 Administrators at a university are planning to offer a

decimal point.
Question 18 The variance of the standard normal distribution is equal to
__________.
Question 19 Employees of a local company are classified according to
gender and job type. The following table summarizes the number of
people in each job category.
Male (M) Female (F)
Job
Administrative (AD) 110 10
Salaried staff (SS) 30 50
Hourly staff (HS) 60 40
If an employee is selected at random, what is the probability that the
employee is female or works as a member of the administration?
the time. For the next 10 products, what is the probability that he makes
fewer than 2 incorrect inspections? Note: Please report your answer with
two places to the right of the decimal, rounding if appropriate.
Question 1 Parameters are known, constant values that are usually
Question 2 In general, an increase in price increases the break even
point if all costs are held constant.
Question 3 If variable costs increase, but price and fixed costs are held
Question 4 Probabilistic techniques assume that no uncertainty exists in
model parameters.
Question 5 If events A and B are independent, then P(A|B) = P(B|A).

Question 6 The events in an experiment are mutually exclusive if only
Question 7 A binomial probability distribution indicates the probability
of r successes in n trials.
Question 8 A model is a functional relationship that includes:
Question 9 If the price increases but fixed and variable costs do not
Question 10 If fixed costs increase, but variable cost and price remain
the same, the break even point
Question 11 A bed and breakfast breaks even every month if they book
30 rooms over the course of a month. Their fixed cost is $4200 per
month and the revenue they receive from each booked room is $180.
What their variable cost per occupied room?
Question 12 The expected value of the standard normal distribution is
equal to
Question 13 In a binomial distribution, for each of n trials, the event
Question 14 The area under the normal curve represents probability,
and the total area under the curve sums to
Question 15 A production run of toothpaste requires a fixed cost of
$100,000. The variable cost per unit is $3.00. If 50,000 units of
toothpaste will be sold during the next month, what sale price must be
chosen in order to break even at the end of the month? Note: please
report the result as a whole number, rounding if necessary and omitting
the decimal point.
Question 16 Administrators at a university are planning to offer a
decimal point.
Question 17 A production process requires a fixed cost of $50,000. The
variable cost per unit is $25 and the revenue per unit is projected to be
$45. Find the break-even point.

Question 18 Wei is considering pursuing an MS in Information Systems
degree. She has applied to two different universities. The acceptance rate
for applicants with similar qualifications is 20% for University X and
45% for University Y. What is the probability that Wei will be accepted
by at least one of the two universities? {Express your answer as a
percent. Round (if necessary) to the nearest whole percent and omit the
decimal. For instance, 20.1% would be written as 20}
Question 19 The variance of the standard normal distribution is equal to
__________.
Question 20 An automotive center keeps tracks of customer complaints
represented as a table (shown below). The random variable xi represents
the number of complaints, and p(xi) is the probability of receiving xi
complaints.
xi 0 1 2 3 4 5 6
p(xi) .10 .15 .18 .20 .20 .10 .07
What is the average number of complaints received per week? Note:
Please report your answer with two places to the right of the decimal,
rounding if appropriate.
************************************

Select one (1) of the following topics for your primary discussion
posting:
Identify the part of setting up a simulation in Excel that you find to be
the most challenging, and explain why.
Identify resources that can help you with that. Explain how simulation is
used in the real world.
Provide a specific example from your own line of work, or a line of
work that you find particularly interesting.
************************************
1. The Hoylake Rescue Squad receives an emergency call every 1, 2, 3,
4, 5, or 6 hours, according to

the following probability distribution. The squad is on duty 24 hours per
day, 7 days per week:
Time Between
a. Simulate the emergency calls for 3 days (note that this will require a
“running” , or cumulative,
hourly clock), using the random number table.
b. Compute the average time between calls and compare this value with
the expected value of the
time between calls from the probability distribution. Why are the result
different?
2. The time between arrivals of cars at the Petroco Services Station is
defined by the following
probability distribution:
Time Between
a. Simulate the arrival of cars at the service station for 20 arrivals and
compute the average time
between arrivals.
b. Simulate the arrival of cars at the service station for 1 hour, using a
different stream of random
numbers from those used in (a) and compute the average time between
arrivals.
c. Compare the results obtained in (a) and (b).
3. The Dynaco Manufacturing Company produces a product in a process
consisting of operations of
five machines. The probability distribution of the number of machines
that will break down in a
week follows:
a. Simulate the machine breakdowns per week for 20 weeks.

b. Compute the average number of machines that will break down per
week.
4. Simulate the following decision situation for 20 weeks, and
recommend the best decision.
A concessions manager at the Tech versus A&M football game must
decide whether to have the
vendors sell sun visors or umbrellas. There is a 30% chance of rain, a
15% chance of overcast skies,
and a 55% chance of sunshine, according to the weather forecast in
college junction, where the
game is to be held. The manager estimates that the following profits will
result from each decision,
given each set of weather conditions:
MAT540 Homework
5. Every time a machine breaks down at the Dynaco Manufacturing
Company (Problem 3), either 1, 2,
or 3 hours are required to fix it, according to the following probability
distribution:
Repair Time (hr.) Probability
Simulate the repair time for 20 weeks and then compute the average
weekly repair time.
************************************
MAT 540 Week 3 Quiz 2 (Two Sets)

Question 1 If two events are not mutually exclusive, then P(A or B) =
P(A) + P(B)
Question 2 Probability trees are used only to compute conditional
probabilities.
Question 3 Seventy two percent of all observations fall within 1 standard
deviation of the mean if the data is normally distributed.
Question 4 Both maximin and minimin criteria are optimistic.
Question 5 The equal likelihood criterion assigns a probability of 0.5 to
each state of nature, regardless of how many states of nature there are.
Question 6 The Hurwicz criterion is a compromise between the minimax
and minimin criteria.
Question 7 Using the minimax regret criterion, we first construct a table
of regrets. Subsequently, for each possible decision, we look across the
states of nature and make a note of the maximum regret possible for that
decision. We then pick the decision with the largest maximum regret.
Find the probability that a randomly selected college student will take
between 2 and 6 minutes to find a parking spot in the main parking lot.
Question 9 The chi-square test is a statistical test to see if an observed
data fit a _________.
Question 10 The metropolitan airport commission is considering the
establishment of limitations on noise pollution around a local airport. At
the present time, the noise level per jet takeoff in one neighborhood near
the airport is approximately normally distributed with a mean of 100
decibels and a standard deviation of 3 decibels. What is the probability
that a randomly selected jet will generate a noise level of more than 105
decibels?

Question 11 A group of friends are planning a recreational outing and
have constructed the following payoff table to help them decide which
activity to engage in. Assume that the payoffs represent their level of
enjoyment for each activity under the various weather conditions.
Weather
Cold Warm Rainy
S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
What is the conservative decision for this situation?
Question 12 A business owner is trying to decide whether to buy, rent,
or lease office space and has constructed the following payoff table
based on whether business is brisk or slow.
The maximin strategy is:
Question 12 The maximin criterion results in the
If the probability of brisk business is .40 and for slow business is .60, the
expected value of perfect information is:
Question 14 A brand of television has a lifetime that is normally
distributed with a mean of 7 years and a standard deviation of 2.5 years.
What is the probability that a randomly chosen TV will last more than 8
years? Note: Write your answers with two places after the decimal,
rounding off as appropriate.
Question 15 A life insurance company wants to update its actuarial
tables. Assume that the probability distribution of the lifetimes of the
years and a standard deviation of 3.5 years. What proportion of the plan
participants are expected to see their 75th birthday? Note: Write your
answers with two places after the decimal, rounding off as appropriate.

Question 16 A manager has developed a payoff table that indicates the
profits associated with a set of alternatives under 2 possible states of
nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
What is the highest expected value? Assume that the probability of S2 is
equal to 0.4.
Question 17 Consider the following decision tree.
What is the expected value for the best decision? Round your answer to
the nearest whole number.
Question 19 If the probability of brisk business is .40, what is the
numerical maximum expected value?
Question 20 The quality control manager for ENTA Inc. must decide
whether to accept (a1), further analyze (a2) or reject (a3) a lot of
incoming material. Assume the following payoff table is available.
Historical data indicates that there is 30% chance that the lot is poor
quality (s1), 50 % chance that the lot is fair quality (s2) and 20% chance
that the lot is good quality (s3).
What is the numerical value of the maximin?
Question 1 If two events are not mutually exclusive, then P(A or B) =
P(A) + P(B)
Question 2 Seventy two percent of all observations fall within 1
standard deviation of the mean if the data is normally distributed.
Question 3 Probability trees are used only to compute conditional
probabilities.
Question 4 Using the minimax regret criterion, we first construct a table
of regrets. Subsequently, for each possible decision, we look across the

states of nature and make a note of the maximum regret possible for that
decision. We then pick the decision with the largest maximum regret.
Question 5 The maximin approach involves choosing the alternative
with the highest or lowest payoff.
Question 6 The Hurwicz criterion is a compromise between the
minimax and minimin criteria.
Question 7 The Hurwicz criterion is a compromise between the
maximax and maximin criteria.
Find the probability that a randomly selected college student will take
between 2 and 6 minutes to find a parking spot in the main parking lot.
Question 9 A professor would like to utilize the normal distribution to
assign grades such that 5% of students receive A's. If the exam average
is 62 with a standard deviation of 13, what grade should be the cutoff for
an A? (Round your answer.
Question 10 The metropolitan airport commission is considering the
establishment of limitations on noise pollution around a local airport. At
the present time, the noise level per jet takeoff in one neighborhood near
the airport is approximately normally distributed with a mean of 100
decibels and a standard deviation of 3 decibels. What is the probability
that a randomly selected jet will generate a noise level of more than 105
decibels?
Question 11 Determining the worst payoff for each alternative and
choosing the alternative with the best worst is called
The maximin strategy is:
If the probability of brisk business is .40 and for slow business is .60, the
expected value of perfect information is

Question 14 The maximin criterion results in the
Question 15 A life insurance company wants to update its actuarial
tables. Assume that the probability distribution of the lifetimes of the
years and a standard deviation of 3.5 years. What proportion of the plan
participants are expected to see their 75th birthday? Note: Write your
answers with two places after the decimal, rounding off as appropriate.
Question 16 A brand of television has a lifetime that is normally
distributed with a mean of 7 years and a standard deviation of 2.5 years.
What is the probability that a randomly chosen TV will last more than 8
years? Note: Write your answers with two places after the decimal,
rounding off as appropriate.
Question 17 If the probability of brisk business is .40, what is the
numerical maximum expected value?
Question 18 A manager has developed a payoff table that indicates the
profits associated with a set of alternatives under 2 possible states of
nature.
Alt S1 S2
1 10 2
2 -2 8
3 8 5
Compute the expected value of perfect information assuming that the
probability of S2 is equal to 0.4.
Question 19 A group of friends are planning a recreational outing and
have constructed the following payoff table to help them decide which
activity to engage in. Assume that the payoffs represent their level of
enjoyment for each activity under the various weather conditions.
Weather
Cold Warm Rainy

S1 S2 S3
Bike: A1 10 8 6
Hike: A2 14 15 2
Fish: A3 7 8 9
Question 20 If the probabilities of cold weather (S1), warm weather
(S2), and rainy weather (S3) are 0.2, 0.4, and 0.4, respectively what is
the EVPI for this situation?
Consider the following decision tree.
What is the expected value for the best decision? Round your answer to
the nearest whole number.
************************************
MAT 540 Week 4 Discussion Forecasting
Methods
Discuss Forecasting Methods
posting:
• Identify any challenges you have in setting up a time-series analysis in
Excel. Explain what they are and why they are challenging. Identify
resources that can help you with that.

• Explain how forecasting is used in the real world. Provide a specific
example from your own line of work, or a line of work that you find
particularly interesting.
************************************
MAT 540 Homework Chapter 15
1. The manager of the Carpet City outlet needs to make an accurate
forecast of the demand for Soft Shag carpet (its biggest seller). If the
manager does not order enough carpet from the carpet mill, customer
will buy their carpet from one of Carpet City’s many competitors. The
manager has collected the following demand data for the past 8 months:
Compute a 3-month moving average forecast for months 4 through 9.
a. Compute a weighted 3-month moving average forecast for months 4
through 9. Assign weights of 0.55, 0.35, and 0.10 to the months in
sequence, starting with the most recent month.
b. Compare the two forecasts by using MAD. Which forecast appears to
be more accurate?

2. The manager of the Petroco Service Station wants to forecast the
demand for unleaded gasoline next month so that the proper number of
gallons can be ordered from the distributor. The owner has accumulated
the following data on demand for unleaded gasoline from sales during
the past 10 months:
a. Compute an exponential smoothed forecast, using an α value of 0.4
b. Compute the MAD.
3. Emily Andrews has invested in a science and technology mutual fund.
Now she is considering liquidating and investing in another fund. She
would like to forecast the price of the science and technology fund for
the next month before making a decision. She has collected the
following data on the average price of the fund during the past 20
months:
a. Using a 3-month average, forecast the fund price for month 21.
b. Using a 3-month weighted average with the most recent month
weighted 0.5, the next most recent month weighted 0.30, and the third
month weighted 0.20, forecast the fund price for month 21.
c. Compute an exponentially smoothed forecast, using α=0.3, and
forecast the fund price for month 21.
d. Compare the forecasts in (a), (b), and (c), using MAD, and indicate
the most accurate.
4. Carpet City wants to develop a means to forecast its carpet sales. The
store manager believes that the store’s sales are directly related to the
number of new housing starts in town. The manager has gathered data

from county records on monthly house construction permits and from
store records on monthly sales. These data are as follows:
Monthly Carpet Sales Monthly Construction
(1,000 yd.) Permits
9 17
14 25
10 8
12 7
15 14
9 7
24 45
21 19
20 28
a. Develop a linear regression model for these data and forecast carpet
sales if 30 construction permits for new homes are filed.
b. Determine the strength of the causal relationship between monthly
sales and new home construction by using correlation.
5. The manager of Gilley’s Ice Cream Parlor needs an accurate forecast
of the demand for ice cream.
The store orders ice cream from a distributor a week ahead; if the store
orders too little, it loses business, and if it orders too much, the extra
must be thrown away. The manager belives that a major determinant of
ice cream sales is temperature (i.e.,the hotter the weather, the more ice
cream people buy). Using an almanac, the manager has determined the
average day time temperature for 14 weeks, selected at random, and

from store records he has determined the ice cream consumption for the
same 14 weeks. These data are summarized as follows:
a. Develop a linear regression model for these data and forecast the ice
cream consumption if the average weekly daytime temperature is
expected to be 85 degrees.
b. Determine the strength of the linear relationship between temperature
and ice cream consumption by using correlation.
c. What is the coefficient of determination? Explain its meaning.
************************************
"Reflection to date Please respond to the following: In a paragraph,
reflect on what you've learned so far in this course. Identify the most
interesting, unexpected, or useful thing you've learned and explain why
************************************

Discuss LP Models
posting:
• The objective function always includes all of the decision variables,
but that is not necessarily true of the constraints. Explain the difference
between the objective function and the constraints. Then, explain why a
constraint need not refer to all the variables.
• Pick any constraint from any problem in the text, and explain how to
plot the line that corresponds to that constraint.
************************************

1. A Cereal Company makes a cereal from several ingredients. Two of
the ingredients, oats and rice,
provide vitamins A and B. The company wants to know how many
ounces of oats and rice it should
include in each box of cereal to meet the minimum requirements of 45
milligrams of vitamin A and
13 milligrams of vitamin B while minimizing cost. An ounce of oats
contributes 10 milligrams of
vitamin A and 2 milligram of vitamin B, whereas an ounce of rice
contributes 6 milligrams of A
and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of
rice costs $0.03.
a. Formulate a linear programming model for this problem.
b. Solve the model by using graphical analysis.
2. A Furniture Company produces chairs and tables from two resources-
labor and wood. The
company has 125 hours of labor and 45 board-ft. of wood available each
day. Demand for chairs is
limited to 5 per day. Each chair requires 7 hours of labor and 3.5 board-
ft. of wood, whereas a table
requires 14 hours of labor and 7 board-ft. of wood. The profit derived
from each chair is $325 and
from each table, $120. The company wants to determine the number of
chairs and tables to produce
each day in order to maximize profit. Formulate a linear programming
model for this problem.
b. Solve the model by using graphical analysis. (Do not round the
answers)
c. How much labor and wood will be unused if the optimal numbers of
chairs and tables are

produced?
3. Kroeger supermarket sells its own brand of canned peas as well as
several national brands. The
store makes a profit of $0.28 per can for its own peas and a profit of
$0.19 for any of the national
brands. The store has 6 square feet of shelf space available for canned
peas, and each can of peas
takes up 9 square inches of that space. Point-of-sale records show that
each week the store never
sales more than half as many cans of its own brand as it does of the
national brands. The store
wants to know how many cans of its own brand of peas of peas and how
many cans of the national
brands to stock each week on the allocated shelf space in order to
maximize profit.
b. Solve the model by using graphical analysis.
MAT540 Homework
4. Solve the following linear programming model graphically:
Minimize Z=8X1 + 6X2
************************************

Discuss sensitivity analysis
posting:
• Identify any challenges you have in setting up a linear programming
problem in Excel, and solving it with Solver. Explain exactly what the
challenges are and why they are challenging. Identify resources that can
help you with that.
• Explain what the shadow price means in a maximization problem.
Explain what this tells us from a management perspective.
************************************
1. Southern Sporting Good Company makes basketballs and footballs.
Each product is produced from
two resources rubber and leather. Each basketball produced results in a
profit of $11 and each

football earns $15 in profit. The resource requirements for each product
and the total resources
available are as follows:
Product
Total resources available 600 900
a. Find the optimal solution.
b. What would be the effect on the optimal solution if the profit for the
basketball changed from
$11 to $12?
c. What would be the effect on optimal solution if 400 additional pounds
of rubber could be
obtained? What would be the effect if 600 additional square feet of
leather could be obtained?
2. A company produces two products, A and B, which have profits of $9
and $7, respectively. Each
unit of product must be processed on two assembly lines, where the
required production times are
as follows:
Product
Resource Requirements per Unit
Line 1 Line 2
A 11 5
B 6 9
Total Hours 65 40
a. Formulate a linear programming model to determine the optimal
product mix that will
maximize profit.
b. What are the sensitivity ranges for the objective function coefficients?
c. Determine the shadow prices for additional hours of production time
on line 1 and line 2 and

indicate whether the company would prefer additional line 1 or line 2
hours.
3. Formulate and solve the model for the following problem:
Irwin Textile Mills produces two types of cotton cloth denim and
corduroy. Corduroy is a heavier
grade of cotton cloth and, as such, requires 8 pounds of raw cotton per
yard, whereas denim
requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4
hours of processing time;
a yard od denim requires 3.0 hours. Although the demand for denim is
practically unlimited, the
maximum demand for corduroy is 510 yards per month. The
manufacturer has 6,500 pounds of
cotton and 3,000 hours of processing time available each month. The
manufacturer makes a profit
of $2.5 per yards of denim and $3.25 per yard of corduroy. The
manufacturer wants to know how
many yards of each type of cloth to produce to maximize profit.
Formulate the model and put it
into standard form. Solve it
a. How much extra cotton and processing time are left over at the
optimal solution? Is the demand
for corduroy met?
b. If Irwin Mills can obtain additional cotton or processing time, but not
both, which should it
select? How much? Explain your answer.
4. The Bradley family owns 410 acres of farmland in North Carolina on
which they grow corn and
tobacco. Each acre of corn costs $105 to plant, cultivate, and harvest;
each acre of tobacco costs

$210. The Bradleys’ have a budget of $52,500 for next year. The
government limits the number
of acres of tobacco that can be planted to 100. The profit from each acre
of corn is $300; the
profit from each acre of tobacco is $520. The Bradleys’ want to know
how many acres of each
crop to plant in order to maximize their profit.
a. Formulate the linear programming model for the problem and solve.
b. How many acres of farmland will not be cultivated at the optimal
solution? Do the Bradleys use
the entire 100-acre tobacco allotment?
c. The Bradleys’ have an opportunity to lease some extra land from a
neighbor. The neighbor is
offering the land to them for $110 per acre. Should the Bradleys’ lease
the land at that price?
What is the maximum price the Bradleys’ should pay their neighbor for
the land, and how
much land should they lease at that price?
MAT540 Homework
d. The Bradleys’ are considering taking out a loan to increase their
budget. For each dollar they
borrow, how much additional profit would they make? If they borrowed
an additional $1,000,
would the number of acres of corn and tobacco they plant change?
************************************
MAT 540 Week 7 Quiz 3 (Three Sets)

Question 1: Graphical solutions to linear programming problems have an
infinite number of possible objective function lines.
Question 2: The following inequality represents a resource constraint for
a maximization problem:
X + Y ≥ 20
Question 3: In minimization LP problems the feasible region is always
below the resource constraints.
Question 4: In a linear programming problem, all model parameters are
assumed to be known with certainty.
Question 5: A feasible solution violates at least one of the constraints.
Question 6: If the objective function is parallel to a constraint, the
constraint is infeasible.
Question 8: Cully furniture buys 2 products for resale: big shelves (B)
and medium shelves (M). Each big shelf costs $500 and requires 100
cubic feet of storage space, and each medium shelf costs $300 and
requires 90 cubic feet of storage space. The company has $75000 to
invest in shelves this week, and the warehouse has 18000 cubic feet
available for storage. Profit for each big shelf is $300 and for each
medium shelf is $150. What is the maximum profit?
Question 9: The following is a graph of a linear programming problem.
The feasible solution space is shaded, and the optimal solution is at the
point labeled Z*.
Which of the following points are not feasible?
Question 10: The production manager for the Coory soft drink company
is considering the production of 2 kinds of soft drinks: regular (R) and

diet(D). Two of the limited resources are production time (8 hours = 480
minutes per day) and syrup limited to 675 gallons per day. To produce a
regular case requires 2 minutes and 5 gallons of syrup, while a diet case
needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are
$3.00 per case and profits for diet soft drink are $2.00 per case. What is
the time constraint?
point labeled Z*.
The equation for constraint DH is:
Question 12: Which of the following statements is not true?
Question 13: In a linear programming problem, a valid objective
function can be represented as
Question 14: The linear programming problem:
MIN Z = 2x1 + 3x2
Subject to: x1 + 2x2 ≤ 20
5x1 + x2 ≤ 40
4x1 +6x2 ≤ 60
x1 , x2 ≥ 0 ,
point labeled Z*.
This linear programming problem is a:
Question 16: A graphical representation of a linear program is shown
below. The shaded area represents the feasible region, and the dashed
line in the middle is the slope of the objective function.
If this is maximization, which extreme point is the optimal solution?
Question 17: Which of the following could be a linear programming
objective function?
Question 18: Solve the following graphically
Max z = 3x1 +4x2
s.t. x1 + 2x2 ≤ 16
2x1 + 3x2 ≤ 18
x1 ≥ 2
x2 ≤ 10

x1, x2 ≥ 0
Find the optimal solution. What is the value of the objective function at
the optimal solution? Note: The answer will be an integer. Please give
your answer as an integer without any decimal point. For example, 25.0
(twenty five) would be written 25
Question 19: Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to: 8x + 5y ≤ 40
0.4x + y ≥ 4
x, y ≥ 0
At the optimal solution, what is the amount of slack associated with the
first constraint?
Question 20: Max Z = $3x + $9y
Subject to: 20x + 32y ≤ 1600
4x + 2y ≤ 240
y ≤ 40
x, y ≥ 0
second constraint?
Question 1: A linear programming problem may have more than one set
of solutions.
Question 3: Graphical solutions to linear programming problems have an
infinite number of possible objective function lines.
Question 4: In a linear programming problem, all model parameters are
assumed to be known with certainty.
Question 5: Surplus variables are only associated with minimization
problems.
Question 6: A linear programming model consists of only decision
variables and constraints.

medium shelf is $150. What is the maximum profit?
point labeled Z*.
This linear programming problem is a:
Question 10: Decision variables
point labeled Z*.
medium shelf is $150. What is the objective function?
point labeled Z*.
The equation for constraint DH is:
point labeled Z*.
Which of the following constraints has a surplus greater than 0?
If this is maximization, which extreme point is the optimal solution?

diet (D). Two of her limited resources are production time (8 hours =
480 minutes per day) and syrup (1 of her ingredients) limited to 675
gallons per day. To produce a regular case requires 2 minutes and 5
gallons of syrup, while a diet case needs 4 minutes and 3 gallons of
syrup. Profits for regular soft drink are $3.00 per case and profits for diet
soft drink are $2.00 per case. What is the objective function?
objective function?
What would be the new slope of the objective function if multiple
optimal solutions occurred along line segment AB? Write your answer
in decimal notation.
Question 19: Max Z = $3x + $9y
Subject to: 20x + 32y ≤ 1600
4x + 2y ≤ 240
y ≤ 40
x, y ≥ 0
second constraint?
Question 20: Solve the following graphically
Max z = 3x1 +4x2
s.t. x1 + 2x2 ≤ 16
2x1 + 3x2 ≤ 18
x1 ≥ 2
x2 ≤ 10
x1, x2 ≥ 0

Question 2: A linear programming model consists of only decision
variables and constraints.
Question 4: In minimization LP problems the feasible region is always
below the resource constraints.
Question 5: Surplus variables are only associated with minimization
problems.
Question 7: A linear programming problem may have more than one set
of solutions.
diet(D). Two of the limited resources are production time (8 hours = 480
minutes per day) and syrup limited to 675 gallons per day. To produce a
regular case requires 2 minutes and 5 gallons of syrup, while a diet case
needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are
$3.00 per case and profits for diet soft drink are $2.00 per case. What is
the time constraint?
is considering the production of 2 kinds of soft drinks: regular and diet.
Two of her limited resources are production time (8 hours = 480 minutes
per day) and syrup (1 of her ingredients) limited to 675 gallons per day.
To produce a regular case requires 2 minutes and 5 gallons of syrup,
while a diet case needs 4 minutes and 3 gallons of syrup. Profits for
regular soft drink are $3.00 per case and profits for diet soft drink are
$2.00 per case. For the production combination of 135 cases of regular
and 0 cases of diet soft drink, which resources will not be completely
used?
Question 10: In a linear programming problem, the binding constraints
for the optimal solution are:

5x1 + 3x2 ≤ 30
2x1 + 5x2 ≤ 20
Which of these objective functions will lead to the same optimal
solution?
Question 11: Which of the following statements is not true?
diet (D). Two of her limited resources are production time (8 hours =
480 minutes per day) and syrup (1 of her ingredients) limited to 675
gallons per day. To produce a regular case requires 2 minutes and 5
gallons of syrup, while a diet case needs 4 minutes and 3 gallons of
syrup. Profits for regular soft drink are $3.00 per case and profits for diet
soft drink are $2.00 per case. What is the objective function?
point labeled Z*.
Question 14: Decision variables
medium shelf is $150. What is the objective function?
objective function?
point labeled Z*.
Which of the following constraints has a surplus greater than 0?
line in the middle is the slope of the objective function. What would be
the new slope of the objective function if multiple optimal solutions

occurred along line segment AB? Write your answer in decimal
notation.
Question 19: Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to: 8x + 5y ≤ 40
0.4x + y ≥ 4
x, y ≥ 0
first constraint?
Question 20: Consider the following minimization problem:
Min z = x1 + 2x2
s.t. x1 + x2 ≥ 300
2x1 + x2 ≥ 400
2x1 + 5x2 ≤ 750
x1, x2 ≥ 0
************************************
MAT 540 Week 8 Assignment Linear
Programming Case Study You are a portfolio
manager for the XYZ investment fund

Week 8 Project
You are a portfolio manager for the XYZ investment fund. The
objective for the fund is to maximize your portfolio returns from the
investments on four alternatives. The investments include (1) stocks, (2)
real estate, (3) bonds, and (4) certificate of deposit (CD). Your total
investment portfolio is $1,000,000.
Investment Returns
Based on the returns from the past five years, you concluded that the
investment annual returns on stocks are 10%, on real estates are 7% on
bonds are 4% and on CD is 1%.
Risk Constraints
However, you also have to analyze the risks associate with each
investment category. A wildly used risk measurement parameter is
called Value at Risk (VaR). (Note: VaR measures the risk of loss on a
specific portfolio of financial assets.) For example, given a million
dollar stock investment, if a portfolio of stocks has a one-day 4% VaR,
there is a 5% probability that the stock portfolio will fall in value by
more than 1,000,000 * 0.004 = $4,000 over a one day period. In the
portfolio, the VaR for stock investments is 6%. Similarly, the VaR for
real estate investment is 2% and the VaR for bond investment is 1% and
the VaR for investment in CD is 0%. To manage the portfolio, you
decided that at 5% probability, your VaR for stocks cannot exceed
$25,000, VaR for real estate cannot exceed $15,000, VaR for bonds
cannot exceed $2,500 and the VaR for CD investment is $0.
Diversification and Liquidity Constraints

As a diversified investment portfolio, you also decided that each
investment category must hold at least $50,000 of the total investment
assets. In addition, you must hold combined CD and bond investment
no less than $200,000 in order to meet liquidity requirement.
The total amount of real estate holding shall not exceed 30% of the
portfolio assets.
A. As a portfolio manager, please formulate and solve the investment
portfolio problem using linear programming technique. What are the
amounts invest in (1) stocks, (2) real estate, (3) bonds and (4) CD?
B. If $500,000 additional investments are available to you in your
portfolio, how would you invest the capital?
C. Would you maintain the portfolio investment if stock yields lowered
to 6%? How would you re-distribute your investment portfolio?
************************************
MAT 540 Week 8 Discussion Practice setting up
linear programming models for business
applications

MAT 540 WEEK 8 DISCUSSION
Practice setting up linear programming models for business applications
Select an even-numbered LP problem from the text, excluding 14, 20,
22, 36 (which are part of your homework assignment). Formulate a
linear programming model for the problem you select.
************************************
1. Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing
for Super Bowl Sunday, and she must determine how much beer to
stock. Betty stocks three brands of beer- Yodel, Shotz, and Rainwater.
The cost per gallon (to the tavern owner) of each brand is as follows:
Brand....................Cost/Gallon
Yodel.....................$1.50
Shotz...................... 0.90
Rainwater............... 0.50
The tavern has a budget of $2,000 for beer for Super Bowl Sunday.
Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon,
and Rainwater at $1.75 per gallon. Based on past football games, Betty
has determined the maximum customer demand to be 400 gallons of

Yodel, 500 gallons of shotz, and 300 gallons of Rainwater. The tavern
has the capacity to stock 1,000 gallons of beer; Betty wants to stock up
completely. Betty wants to determine the number of gallons of each
brand of beer to order so as to maximize profit.
b. Solve the model by using the computer.
2. As result of a recently passed bill, a congressman’s district has been
allocated $3 million for programs and projects. It is up to the
congressman to decide how to distribute the money. The congressman
has decide to allocate the money to four ongoing programs because of
their importance to his district- a job training program, a parks project, a
sanitation project, and a mobile library. However, the congressman
wants to distribute the money in a manner that will please the most
voters, or, in other words, gain him the most votes in the upcoming
election. His staff’s estimates of the number of votes gained per dollar
spent for the various programs are as follows.
Program....................Votes/Dollar
Job training................0.03
Parks.............................0.08
Sanitation....................0.05
Mobile library.............0.03
In order also to satisfy several local influential citizens who financed his
election, he is obligated to observe the following guidelines:
• None of the programs can receive more than 30% of the total
allocation
• The amount allocated to parks cannot exceed the total allocated to both
the sanitation project and the mobile library.
• The amount allocated to job training must at least equal the amount
spent on the sanitation project. Any money not spent in the district will
be returned to the government; therefore, the congressman wants to
spend it all. Thee congressman wants to know the amount to allocate to
each program to maximize his votes.

3. Anna Broderick is the dietician for the State University football team,
and she is attempting to determine a nutritious lunch menu for the team.
She has set the following nutritional guidelines for each lunch serving:
• Between 1,300 and 2,100 calories
• At least 4 mg of iron
• At least 15 but no more than 55g of fat
• At least 30g of protein
• At least 60g of carbohydrates
• No more than 35 mg of cholesterol
She selects the menu from seven basic food items, as follows, with the
nutritional contributions per pound and the cost as given:
............ Calories......Iron....Protein
...Carbohydrates....Fat....Cholesterol......Cost
............. (Per lb).......(mg/lb).....(g/lb)........(g/lb)..............(g/lb).........
(mg/lb)..........($/lb)
Chicken 500 4.2 17 0 30 180 0.85
Fish 480 3.1 85 0 5 90 3.35
Ground beef 840 0.25 82 0 75 350 2.45
Dried beans 590 3.2 10 30 3 0 0.85
Lettuce 40 0.4 6 0 0 0 0.70
Potatoes 450 2.25 10 70 0 0 0.45
Milk (2%) 220 0.2 16 22 10 20 0.82
The dietician wants to select a menu to meet the nutritional guidelines
while minimizing the total cost per serving.
a. Formulate a linear programming model for this problem and solve.
b. If a serving of each of the food items (other than milk) was limited to
no more than a half pound, what effect would this have on the solution?
4. Dr. Maureen Becker, the head administrator at Jefferson County
Regional Hospital, must determine a schedule for nurses to make sure
there are enough of them on duty throughout the day. During the day,
the demand for nurses varies. Maureen has broken the day in to twelve
2- hour periods. The slowest time of the day encompasses the three
periods from 12:00 A.M. to 6:00 A.M., which beginning at midnight;

require a minimum of 30, 20, and 40 nurses, respectively. The demand
for nurses steadily increases during the next four daytime periods.
Beginning with the 6:00 A.M.- 8:00 A.M. period, a minimum of 50, 60,
80, and 80 nurses are required for these four periods, respectively. After
2:00 P.M. the demand for nurses decreases during the afternoon and
evening hours. For the five 2-hour periods beginning at 2:00 P.M. and
ending midnight, 70, 70, 60, 50, and 50 nurses are required, respectively.
A nurse reports for duty at the beginning of one of the 2-hour periods
and works 8 consecutive hours (which is required in the nurses’
contract). Dr. Becker wants to determine a nursing schedule that will
meet the hospital’s minimum requirement throughout the day while
using the minimum number of nurses.
5. The production manager of Videotechnics Company is attempting to
determine the upcoming 5-month production schedule for video
recorders. Past production records indicate that 2,000 recorders can be
produced per month. An additional 600 recorders can be produced
monthly on an overtime basis. Unit cost is $10 for recorders produced
during regular working hours and $15 for those produced on an overtime
basis. Contracted sales per month are as follows: Month Contracted
Sales (units) 1 1200 2 2100 3 4 5 2400 3000 4000 Inventory carrying
costs are $2 per recorder per month. The manager does not want any
inventory carried over past the fifth month. The manager wants to know
the monthly production that will minimize total production and
inventory costs. a. Formulate a linear programming model for this
problem. b. Solve the model by using the computer.
************************************

MAT 540 Week 9 Discussion Application of
Integer Programming
Week 9 Discussion
Explain how the applications of Integer programming differ from those
of linear programming. Give specific instances in which you would use
an integer programming model rather than an LP model. Provide real-
world examples.
************************************
MAT 540 Week 9 Homework - Chapter 5

1. Rowntown Cab Company has 70 drivers that it must schedule in
three 8-hour shifts. However, the demand for cabs in the metropolitan
area varies dramatically according to time of the day. The slowest period
is between midnight and 4:00 A.M. the dispatcher receives few calls,
and the calls that are received have the smallest fares of the day. Very
few people are going to the airport at that time of the night or taking
other long distance trips. It is estimated that a driver will average $80 in
fares during that period. The largest fares result from the airport runs in
the morning. Thus, the drivers who sart their shift during the period from
4:00 A.M. to 8:00 A.M. average $500 in total fares, and drivers who
start at 8:00 A.M. average $420. Drivers who start at noon average $300,
and drivers who start at 4:00 P.M. average $270. Drivers who start at the
beginning of the 8:00 P.M. to midnight period earn an average of $210
in fares during their 8-hour shift.
To retain customers and acquire new ones, Rowntown must maintain a
high customer service level. To do so, it has determined the minimum
number of drivers it needs working during every 4-hour time segment-
10 from midnight to 4:00 A.M. 12 from 4:00 to 8:00 A.M. 20 from 8:00
A.M. to noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M.,
and 18 from 8:00 P.M. to midnight.
a. Formulate and solve an integer programming model to help
Rowntown Cab schedule its drivers.
b. If Rowntown has a maximum of only 15 drivers who will work the
late shift from midnight to 8:00 A.M., reformulate the model to reflect
this complication and solve it
c. All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M.,
so the company has decided to limit the number of drivers who work this
8-hour shift to 20. Reformulate the model in (b) to reflect this restriction
and solve it.
2.
2. Juan Hernandez, a Cuban athlete who visits the United States and
Europe frequently, is allowed to return with a limited number of
consumer items not generally available in Cuba. The items, which are
carried in a duffel bag, cannot exceed a weight of 5 pounds. Once Juan

is in Cuba, he sells the items at highly inflated prices. The weight and
profit (in U.S. dollars) of each item are as follows: Item Weight (lb.)
Profit Denim jeans 2 $90 CD players 3 150 Compact discs 1 30 Juan
wants to determine the combination of items he should pack in his duffel
bag to maximize his profit. This problem is an example of a type of
integer programming problem known as a
“knapsack” problem. Formulate and solve the problem.
3. The Texas Consolidated Electronics Company is contemplating a
research and development program encompassing eight research
projects. The company is constrained from embarking on all projects by
the number of available management scientists (40) and the budget
available for R&D projects ($300,000). Further, if project 2 is selected,
project 5 must also be selected (but not vice versa). Following are the
resources requirement and the estimated profit for each project.
Project Expense Management Estimated Profit ($1,000s) Scientists
required (1,000,000s) 1 50 6 0.30 2 105 8 0.85 3 56 9 0.20 4 45 3 0.15 5
90 7 0.50 6 80 5 0.45 7 78 8 0.55 8 60 5 0.40 Formulate the integer
programming model for this problem and solve it using the computer.
Corsouth Mortgage Associates is a large home mortgage firm in the
southeast. It has a poll of permanent and temporary computer operators
who process mortgage accounts, including posting payments and
updating escrow accounts for insurance and taxes. A permanent operator
can process 220 accounts per day, and a temporary operator can process
140 accounts per day. On average, the firm must process and update at
least 6,300 accounts daily. The company has 32 computer workstations
available. Permanent and temporary operators work 8 hours per day. A
permanent operator averages about 0.4 error per day, whereas a
temporary operator averages 0.9 error per day. The company wants to
limit errors to 15 per day. A permanent operator is paid $120 per day
wheras a temporary operator is paid $75 per day. Corsouth wants to
determine the number of permanent and temporary operators it needs to
minimize cost. Formulate, and solve an integer programming model for
this problem and compare this solution to the non-integer solution.

5. Globex Investment Capital Corporation owns six companies that have
the following estimated returns (in millions of dollars) if sold in one of
the next 3 years:
Year Sold (estimated returns, $1,000,000s) Company 1 2 3 1 $14 $18
$232 9 11 153 18 23 274 16 21 255 12 16 226 21 23 28 To generate
operating funds, the company must sell at least $20 million worth of
assets in year 1, $25 million in year 2, and $35 million in year 3. Globex
wants to develop a plan for selling these companies during the next 3
years to maximize return.
Formulate an integer programming model for this problem and solve it
by using the computer.
************************************
MAT 540 Week 9 Quiz 4 Set (Three Sets)
Question 1: When using a linear programming model to solve the "diet"
problem, the objective is generally to maximize profit.
Question 2: In a balanced transportation model, supply equals demand
such that all constraints can be treated as equalities.
Question 3: In a transportation problem, a demand constraint (the
amount of product demanded at a given destination) is a less-than-or
equal-to constraint (≤).

Question 4: Fractional relationships between variables are permitted in
the standard form of a linear program.
Question 5: The standard form for the computer solution of a linear
programming problem requires all variables to be to the right and all
numerical values to be to the left of the inequality or equality sign
Question 6: A systematic approach to model formulation is to first
construct the objective function before determining the decision
variables.
Question 7: A croissant shop produces 2 products: bear claws (B) and
almond filled croissants (C). Each bear claw requires 6 ounces of flour,
1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant
requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste.
The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800
TS of almond paste available for today's production run. Bear claw
profits are 20 cents each, and almond filled croissant profits are 30 cents
each. What is the optimal daily profit?
Question 8: In a portfolio problem, X1, X2, and X3 represent the
number of shares purchased of stocks 1, 2, an 3 which have selling
prices of $15, $47.25, and $110, respectively. The investor stipulates
that stock 1 must not account for more than 35% of the number of shares
purchased. Which constraint is correct?
Question 9: Balanced transportation problems have the following type of
constraints:
Question 10: The production manager for the Softy soft drink company
Two of her resources are production time (8 hours = 480 minutes per
day) and syrup (1 of the ingredients) limited to 675 gallons per day. To
produce a regular case requires 2 minutes and 5 gallons of syrup, while a
diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft
drink are $3.00 per case and profits for diet soft drink are $2.00 per case.
What is the time constraint?
Question 12: The following types of constraints are ones that might be
found in linear programming formulations:
1. ≤

2. =
3. >
Question 13: The owner of Chips etc. produces 2 kinds of chips: Lime
(L) and Vinegar (V). He has a limited amount of the 3 ingredients used
to produce these chips available for his next production run: 4800
ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of
Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of
herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt,
8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips
are $0.40, and for a bag of Vinegar chips $0.50.
What is the constraint for salt?
Question 14: Small motors for garden equipment is produced at 4
manufacturing facilities and needs to be shipped to 3 plants that produce
different garden items (lawn mowers, rototillers, leaf blowers). The
company wants to minimize the cost of transporting items between the
facilities, taking into account the demand at the 3 different plants, and
the supply at each manufacturing site. The table below shows the cost to
ship one unit between each manufacturing facility and each plant, as
well as the demand at each plant and the supply at each manufacturing
facility.
What is the demand constraint for plant B?
Question 15: Compared to blending and product mix problems,
transportation problems are unique because
Question 16: Assume that x2, x7 and x8 are the dollars invested in three
different common stocks from New York stock exchange. In order to
diversify the investments, the investing company requires that no more
than 60% of the dollars invested can be in "stock two". The constraint
for this requirement can be written as:
Question 17: The owner of Black Angus Ranch is trying to determine
the correct mix of two types of beef feed, A and B which cost 50 cents
and 75 cents per pound, respectively. Five essential ingredients are
contained in the feed, shown in the table below. The table also shows
the minimum daily requirements of each ingredient.

The constraint for ingredient 3 is:
Question 18: Let xij = gallons of component i used in gasoline j. Assume
that we have two components and two types of gasoline. There are 8,000
gallons of component 1 available, and the demand gasoline types 1 and 2
are 11,000 and 14,000 gallons respectively. Write the supply constraint
for component 1.
Question 19: Quickbrush Paint Company makes a profit of $2 per gallon
on its oil-base paint and $3 per gallon on its water-base paint. Both
paints contain two ingredients, A and B. The oil-base paint contains 90
percent A and 10 percent B, whereas the water-base paint contains 30
percent A and 70 percent B. Quickbrush currently has 10,000 gallons of
ingredient A and 5,000 gallons of ingredient B in inventory and cannot
obtain more at this time. The company wishes to use linear
programming to determine the appropriate mix of oil-base and water-
base paint to produce to maximize its total profit. How many gallons of
water based paint should the Quickbrush make? Note: Please express
your answer as a whole number, rounding the nearest whole number, if
appropriate.
Question 20: Kitty Kennels provides overnight lodging for a variety of
pets. An attractive feature is the quality of care the pets receive,
including well balanced nutrition. The kennel's cat food is made by
mixing two types of cat food to obtain the "nutritionally balanced cat
diet." The data for the two cat foods are as follows:
Kitty Kennels wants to be sure that the cats receive at least 5 ounces of
protein and at least 3 ounces of fat per day. What is the cost of this plan?
Express your answer with two places to the right of the decimal point.
For instance, $9.32 (nine dollars and thirty-two cents) would be written
as 9.32

Question 1: In a transportation problem, a demand constraint (the
amount of product demanded at a given destination) is a less-than-or
equal-to constraint (≤).
Question 2: A constraint for a linear programming problem can never
have a zero as its right-hand-side value.
Question 3: Product mix problems cannot have "greater than or equal to"
(≥) constraints.
Question 4: In formulating a typical diet problem using a linear
programming model, we would expect most of the constraints to be
related to calories.
for component 1.

Question 11: Balanced transportation problems have the following type
of constraints:
prices of $15, $47.25, and $110, respectively. The investor has up to
$50,000 to invest. The expected returns on investment of the three stocks
are 6%, 8%, and 11%. An appropriate objective function is
1. ≤
2. =
3. >
$50,000 to invest. The stockbroker suggests limiting the investments so
that no more than $10,000 is invested in stock 2 or the total number of
shares of stocks 2 and 3 does not exceed 350, whichever is more
restrictive. How would this be formulated as a linear programming
constraint?
Question 15: The owner of Black Angus Ranch is trying to determine
the correct mix of two types of beef feed, A and B which cost 50 cents
and 75 cents per pound, respectively. Five essential ingredients are
contained in the feed, shown in the table below. The table also shows
the minimum daily requirements of each ingredient.
Ingredient Percent per pound in Feed A Percent per pound in Feed B
Minimum daily requirement (pounds)
1 20 24 30
2 30 10 50
3 0 30 20
4 24 15 60
5 10 20 40

The constraint for ingredient 3 is:
Two of her resources are constraint production time (8 hours = 480
minutes per day) and syrup (1 of her ingredient) limited to 675 gallons
per day. To produce a regular case requires 2 minutes and 5 gallons of
syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits
for regular soft drink are $3.00 per case and profits for diet soft drink are
$2.00 per case. What is the optimal daily profit?
Question 18: If Xij = the production of product i in period j, write an
expression to indicate that the limit on production of the company's 3
products in period 2 is equal to 400.
as 9.32

oil based paint should the Quickbrush make? Note: Please express your
answer as a whole number, rounding the nearest whole number, if
appropriate.
Question 1: A constraint for a linear programming problem can never
have a zero as its right-hand-side value.
Question 3: In a media selection problem, instead of having an objective
of maximizing profit or minimizing cost, generally the objective is to
maximize the audience exposure.
Question 4: The standard form for the computer solution of a linear
programming problem requires all variables to be to the right and all
numerical values to be to the left of the inequality or equality sign
Question 6: Fractional relationships between variables are permitted in
the standard form of a linear program.
Question 7: Assume that x2, x7 and x8 are the dollars invested in three
different common stocks from New York stock exchange. In order to
diversify the investments, the investing company requires that no more
than 60% of the dollars invested can be in "stock two". The constraint
for this requirement can be written as:
$50,000 to invest. The stockbroker suggests limiting the investments so
that no more than $10,000 is invested in stock 2 or the total number of
shares of stocks 2 and 3 does not exceed 350, whichever is more

restrictive. How would this be formulated as a linear programming
constraint?
Question 10: Balanced transportation problems have the following type
of constraints:
Question 11: Compared to blending and product mix problems,
transportation problems are unique because
1. ≤
2. =
3. >

for component 1.
Question 17: When systematically formulating a linear program, the first
step is
$50,000 to invest. The expected returns on investment of the three stocks
are 6%, 8%, and 11%. An appropriate objective function is
oil based paint should the Quickbrush make? Note: Please express your
answer as a whole number, rounding the nearest whole number, if
appropriate.
as 9.32
************************************

MAT 540 Week 10 Discussion Transshipment
problems
Discussion assignment and transshipment problems
posting:
• Explain the assignment model and how it facilitates in solving
transportation problems. Determine the benefits to be gained from using
this model.
• Identify any challenges you have in setting up an transshipment model
in Excel, and solving it with Solver. Explain exactly what the challenges
are and why they are challenging. Identify resources that can help you
with that.
************************************

1. Consider the following transportation problem:
From To (Cost) Supply 1 2 3 A 6 5 5 150 B 11 8 9 85 C 4 10 7 125
Demand 70 100 80
Formulate this problem as a linear programming model and solve it by
the using the computer.
2. Consider the following transportation problem:
From To (Cost) Supply 1 2 3 A 8 14 8 120 B 6 17 7 80 C 9 24 10 150
Demand 110 140 100 Solve it by using the computer.
3. World foods, Inc. imports food products such as meats, cheeses, and
pastries to the United States from warehouses at ports in Hamburg,
Marseilles and Liverpool. Ships from these ports deliver the products to
Norfolk, New York and Savannah, where they are stored in company
warehouses before being shipped to distribution centers in Dallas, St.
Louis and Chicago. The products are then distributed to specialty foods
stores and sold through catalogs. The shipping costs ($/1,000 lb.) from
the European ports to the U.S. cities and the available supplies (1000 lb.)
at the European ports are provided in the following table: From To
(Cost) Supply 4. Norfolk 5. New York 6. Savannah 1. Hamburg 320
280 555 75 2. Marseilles 410 470 365 85 3. Liverpool 550 355 525 40
The transportation costs ($/1000 lb.) from each U.S. city of the three
distribution centers and the demands (1000 lb.) at the distribution centers
are as follows:
Warehouse Distribution Center 7. Dallas 8. St. Louis 9. Chicago 4.
Norfolk 80 78 85 5. New York 100 120 95 6. Savannah 65 75 90
Demand 85 70 65 Determine the optimal shipments between the

European ports and the warehouses and the distribution centers to
minimize total transportation costs.
4. The Omega Pharmaceutical firm has five salespersons, whom the firm
wants to assign to five sales regions. Given their various previous
contacts, the sales persons are able to cover the regions in different
amounts of time. The amount of time (days) required by each
salesperson to cover each city is shown in the following table:
Salesperson Region (days) A B C D E 1 20 10 12 10 22 2 14 10 18 11
15 3 12 13 19 11 14 4 16 12 14 22 16 5 12 15 19 26 23 Which
salesperson should be assigned to each region to minimize total time?
Identify the optimal assignments and compute total minimum time.
************************************
MAT 540 Week 10 Quiz 5 (Three Sets)
Question 1: Rounding non-integer solution values up to the nearest
integer value will result in an infeasible solution to an integer linear
programming problem.

Question 2: The solution to the LP relaxation of a maximization integer
linear program provides an upper bound for the value of the objective
function.
Question 3: If we are solving a 0-1 integer programming problem with
three decision variables, the constraint x1 + x2 ≤ 1 is a mutually
exclusive constraint.
Question 4: A conditional constraint specifies the conditions under
which variables are integers or real variables.
three decision variables, the constraint x1 + x2 + x3 ≤ 3 is a mutually
Question 6: If exactly 3 projects are to be selected from a set of 5
projects, this would be written as 3 separate constraints in an integer
program.
Question 7: The Wiethoff Company has a contract to produce 10000
garden hoses for a customer. Wiethoff has 4 different machines that can
produce this kind of hose. Because these machines are from different
manufacturers and use differing technologies, their specifications are not
the same.
Write the constraint that indicates they can purchase no more than 3
machines.
Question 8: In a 0-1 integer programming model, if the constraint x1-x2
= 0, it means when project 1 is selected, project 2 __________ be
selected.
Question 9: Assume that we are using 0-1 integer programming model to
solve a capital budgeting problem and xj = 1 if project j is selected and
xj = 0, otherwise.
The constraint (x1 + x2 + x3 + x4 ≤ 2) means that __________ out of
the 4 projects must be selected.
Question 10: If we are solving a 0-1 integer programming problem, the
constraint x1 + x2 ≤ 1 is a __________ constraint.
constraint x1 = x2 is a __________ constraint.
Question 12: If the solution values of a linear program are rounded in
order to obtain an integer solution, the solution is

constraint x1 + x2 = 1 is a __________ constraint.
constraint x1 ≤ x2 is a __________ constraint.
Question 15: Binary variables are
Question 16: In a 0-1 integer programming model, if the constraint x1-
x2 ≤ 0, it means when project 2 is selected, project 1 __________ be
selected.
Question 17: The solution to the linear programming relaxation of a
minimization problem will always be __________ the value of the
integer programming minimization problem.
Question 18: In a __________ integer model, some solution values for
decision variables are integers and others can be non-integer.
Question 19: Max Z = 3x1 + 5x2
Subject to: 7x1 + 12x2 ≤ 136
3x1 + 5x2 ≤ 36
x1, x2 ≥ 0 and integer
the optimal solution. Note: The answer will be an integer. Please give
(twenty-five) would be written 25
Question 20: Consider the following integer linear programming
problem
Max Z = 3x1 + 2x2
Subject to: 3x1 + 5x2 ≤ 30
5x1 + 2x2 ≤ 28
x1 ≤ 8
x1 ,x2 ≥ 0 and integer

program.
Question 3: Rounding non-integer solution values up to the nearest
integer value will result in an infeasible solution to an integer linear
programming problem.
constraint x1 ≤ x2 is a conditional constraint.
three decision variables, the constraint x1 + x2 ≤ 1 is a mutually
Question 6: In a problem involving capital budgeting applications, the 0-
1 variables designate the acceptance or rejection of the different projects.
the same.
Write a constraint to ensure that if machine 4 is used, machine 1 will not
be used.
Question 8: You have been asked to select at least 3 out of 7 possible
sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6,
and S7. The restrictions are:
Restriction 1. Evaluating sites S1 and S3 will prevent you from
exploring site S7.
Restriction 2. Evaluating sites S2 or
S4 will prevent you from assessing site S5.
Restriction 3. Of all the sites, at least 3 should be assessed.
Assuming that Si is a binary variable, write the constraint(s) for the
second restriction

Question 9: In a 0-1 integer programming model, if the constraint x1-x2
= 0, it means when project 1 is selected, project 2 __________ be
selected.
Subject to: 17x1 + 8x2 ≤ 136
3x1 + 4x2 ≤ 36
What is the optimal solution?
constraint x1 ≤ x2 is a __________ constraint.
Question 12: Assume that we are using 0-1 integer programming model
to solve a capital budgeting problem and xj = 1 if project j is selected
and xj = 0, otherwise.
selected.
the same.
Write the constraint that indicates they can purchase no more than 3
machines.
exploring site S7.

Assuming that Si is a binary variable, the constraint for the first
restriction is
problem
Max Z = 3x1 + 2x2
4x1 + 2x2 ≤ 28
x1 ≤ 8
x1 , x2 ≥ 0 and integer
problem
Max Z = 3x1 + 2x2
5x1 + 2x2 ≤ 28
x1 ≤ 8
x1 ,x2 ≥ 0 and integer
Question 1: In a problem involving capital budgeting applications, the 0-
1 variables designate the acceptance or rejection of the different projects.

program.
Question 4: In a 0-1 integer programming problem involving a capital
budgeting application (where xj = 1, if project j is selected, xj = 0,
otherwise) the constraint x1 - x2 ≤ 0 implies that if project 2 is selected,
project 1 can not be selected.
Question 5: In a mixed integer model, some solution values for decision
variables are integer and others are only 0 or 1.
constraint x1 ≤ x2 is a conditional constraint.
exploring site S7.
Assuming that Si is a binary variable, write the constraint(s) for the
second restriction
Question 9: In a capital budgeting problem, if either project 1 or project
2 is selected, then project 5 cannot be selected. Which of the alternatives
listed below correctly models this situation?
selected.
Question 11: In a __________ integer model, some solution values for
decision variables are integers and others can be non-integer.

Question 12: Assume that we are using 0-1 integer programming model
to solve a capital budgeting problem and xj = 1 if project j is selected
and xj = 0, otherwise.
constraint x1 + x2 ≤ 1 is a __________ constraint.
exploring site S7.
Assuming that Si is a binary variable, the constraint for the first
restriction is
Subject to: 17x1 + 8x2 ≤ 136
3x1 + 4x2 ≤ 36
What is the optimal solution?
constraint x1 = x2 is a __________ constraint.
Subject to: 7x1 + 12x2 ≤ 136
3x1 + 5x2 ≤ 36

problem
Max Z = 3x1 + 2x2
4x1 + 2x2 ≤ 28
x1 ≤ 8
x1 , x2 ≥ 0 and integer
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