Math 540 Massive Success / snaptutorial.com
- 1. MATH 540 quiz 3 (7) For more classes visit www.snaptutorial.com Question 1 A linear programming model consists of only decision variables and constraints. Question 2 In a linear programming problem, all model parameters are assumed to be known with certainty. Question 3 A linear programming problem may have more than one set of solutions.
- 2. Question 4 In minimization LP problems the feasible region is always below the resource constraints. 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 7 Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
- 3. Question 8 ) Which of the following could be a linear programming objective function? Question 9 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? Question 10 In a linear programming problem, a valid objective function can be represented as
- 4. Question 11 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 12 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 constraints has a surplus greater than 0? Question 13 Which of the following statements is not true?
- 5. Question 14 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 objective function? Question 15 The production manager for the Coory soft drink company 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 16
- 6. 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*. The equation for constraint DH is: Question 17 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 a maximization, which extreme point is the optimal solution? Question 18
- 7. 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. What would be the new slope of the objective function if multiple optimal solutions occurred along line segment AB? Write your in decimal notation. Evaluation Method Correct Case Sensitivity Exact Match -1.5 Exact Match - 1.5 Question 19 Max Z = $3x + $9y Subject to: 20x + 32y ≤ 1600 4x + 2y ≤ 240 y ≤ 40
- 8. x, y ≥ 0 At the optimal solution, what is the amount of slack associated with the second constraint? Evaluation Method Correct Case Sensitivity Exact Match 96 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
- 9. Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The will be an integer. Please give your as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25 Evaluation Method Correct Case Sensitivity Exact Match 27 ============================== MATH 540 Quiz 4 Chp. 3 For more classes visit www.snaptutorial.com Question 1 A systematic approach to model formulation is to first construct the objective function before determining the decision variables. • Question 2
- 10. 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 a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). • Question 5 In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.
- 11. • Question 6 In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories. • Question 7 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 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,
- 12. $47.25, and $110, respectively. The investor has up to $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 9 The following types of constraints are ones that might be found in linear programming formulations: 1. ≤ 2. = 3. > • Question 10 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?
- 13. • Question 11 The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. 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 12 A systematic approach to model formulation is to first • 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
- 14. 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 Compared to blending and product mix problems, transportation problems are unique because • Question 15 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. • Question 16 Balanced transportation problems have the following type of constraints:
- 15. • 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. 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:
- 16. • 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 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 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 20
- 17. 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 oil based paint should the Quickbrush make? Note: Please express your as a whole number, rounding the nearest whole number, if appropriate. ===============================