Math 133 – unit 2 individual project name/tutorialoutlet

MATH 133 – Unit 2 Individual Project NAME
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MATH 133 – Unit 2 Individual Project NAME (Required):
_____________________________
Please show all work details with answers, insert the graph, and provide
answers to all of the critical thinking questions on this document.
Suppose you have a startup company that develops and sells a gaming
app for smartphones. You
get to know the financial performance of this by understanding your
cost, revenue and profit.
The monthly cost function (in US dollars) of developing your app is C
( x )=2 x+ b , where
C ( x ) is the cost and x is the number of app downloads. The $2 in the
equation is called the variable cost per gaming app download and b is
called the fixed cost.
The monthly revenue function (in US dollars), based on previous
monthly sales, is modeled by
2
the function, R ( x ) =−0.6 x +362 x , 0 ≤ x ≤300.
The monthly profit function (in US dollars),

the revenue, i.e. P ( x ) , is derived by subtracting the cost from P ( x )=R
( x )−C ( x ) . For each question, be sure to show all your work details
for full credit. When applicable,
round all value answers to the nearest cent. First letter of your last
name
A-F
G-L
M-R
S-Z Possible values for b
$1,000 - $1,500
$1,501 - $2,000
$2,001 - $2,500
$2,501 - $3,000 1. Based on the first letter of your LAST name, choose a
value for your fixed cost, b. Use
your chosen value of b to write your cost function, C( x ) . Then use
P ( x )=R ( x )−C ( x ) , to write your simplified profit function? (Show
your work details.)
2. Using the vertex formula (-b/2a), at how many downloads would your
company achieve a
maximum profit? How much is this maximum profit? (Show your work
details)
3. How many downloads would give you a profit of $20,000 the next
month? (Show your

work details. Hint: Let the profit function be equal to $20,000 and solve
for x using the Page 1 of 2 quadratic formula. Since the domain of the
Profit function is [0,300], be sure your value
of x is between 0 and 300.)
4. Complete the table below by calculating the profit for each number of
downloads. (Show
your work details for x=50 and x=200 , ONLY.)
x, number of downloads
0
50
100
200
300 P(x), profit in US dollars 5. Using the table from part 4, generate a
graph of your profit function using Excel or
another graphing utility. (There are free downloadable programs like
Graph 4.4.2 or
Microsoft’s Mathematics 4.0; or online utilities like this site ; and there
are many others.)
Insert the graph into the supplied Student Answer Form. Be sure to label
and number
the axes appropriately so that the graph matches the chosen and
calculated values
from above. Your graph will be only a part of a parabola since the
domain of this

quadratic function is [0, 300].
6. Do you think developing a mathematical model of a profit function
such as the one in this
assignment can help a company to understand its start-up dynamics?
Explain the
reasoning that led to your conclusion.
References
Desmos. (n.d.). Retrieved from https://www.desmos.com/
Graph 4.4.2. (n.d.). Retrieved from the Graph Web site:
http://www.padowan.dk/
Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site:
https://www.microsoft.com/en-us/default.aspx Page 2 of 2
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