MATH133 – Unit 2 Point Values:Question

Point-value

1

20

2

20

3

20

4

20

5

20

Total

100

You earned

Comments

MATH133 – Unit 2 Individual Project

NAME (Required): ______________________

Assignment Instructions:

1. For each question, show all of your work for full credit.

2. Insert all labeled and titled graphs by using screenshots from Excel or desmos.com as

described in the Unit 1 Discussion Board (or other graph program).

3. Provide final answers to all questions in the boxes provided.

4. Round all value answers to 3 decimal places, unless otherwise noted.

Use the following scenario for questions 1 – 2

You have a start-up company that develops and sells a gaming app for smartphones. You need

to analyze your company’s financial performance by understanding your cost, revenue, and

profit (in U.S. dollars).

The monthly cost function of developing your app is as follows:

𝐶(𝑥) = 3𝑥 + ℎ

where

𝐶(𝑥) is the cost

𝑥 is the number of app downloads

$3 is the variable cost per gaming app download

h is the fixed cost

Page 1 of 6

The monthly revenue function, based on previous monthly sales, is modeled by the following

function:

𝑅(𝑥) = −0.4𝑥 2 + 360𝑥, 0 ≤ 𝑥 ≤ 600

The monthly profit function (in U.S. dollars), 𝑃(𝑥), is derived by subtracting the cost from the

revenue, that is

𝑃(𝑥) = 𝑅(𝑥) − 𝐶(𝑥)

1. Based on the first letter of your last name, choose a value for your fixed cost, h.

First letter of your

last name

A–F

G–L

M–R

S–Z

Possible values for h

$4,000–4,500

$4,501–5,000

$5,001–5,500

$5,501–$6,000

Use your chosen value for ℎ to write your cost function, 𝐶(𝑥).

Then, use 𝑃(𝑥) = 𝑅(𝑥) − 𝐶(𝑥) to write your simplified profit function.

(20 points)

Chosen h

Cost function C(x)

Final answer for P(x)

Show your work below:

Page 2 of 6

2. The P(x) equation you determined in problem 1 is a quadratic equation of the following

form:

𝑎𝑥 2 + 𝑏𝑥 + 𝑐

where

a is the coefficient for 𝑥 2

b is the coefficient for x

c is the constant

For this equation, the maximum profit occurs when the number of downloads is

x = -b/(2a)

At how many downloads would your company achieve a maximum profit?

How much is this maximum profit? (20 points)

Number of downloads

Whole number

Maximum profit

Round to 2 decimal places

Show your work below:

Page 3 of 6

3. If the profit was given by 𝑃(𝑥) = −0.5x 2 + 400𝑥 − 6,000, how many downloads would give

you a profit of $30,000 the next month? (20 points)

Hint: Let the profit function be equal to $30,000, and solve for x using the quadratic

formula. Because the domain of the profit function is [0, 600], be sure that the value of

𝑥 is between 0 and 600.

Number of downloads

Round to whole number

Show your work below:

Page 4 of 6

4. Assume that the profit is given by the following:

𝑃(𝑥) = −0.5𝑥 2 + 400𝑥 − 6,000

Complete the following table by calculating the profit for each number of downloads.

(20 points)

x, Number of

downloads

P(x), Profit in U.S. dollars

Round to 2 decimal places

20

50

100

200

300

Show your work below for 𝒙 = 𝟓𝟎 and 𝒙 = 𝟐𝟎𝟎 only:

Page 5 of 6

5. Generate a graph of the following profit equation:

𝑃(𝑥) = −0.5𝑥 2 + 400𝑥 − 6,000

Graph your function using desmos.com, Excel, or any similar online utilities. An

introduction to desmos.com can be found at http://learn.desmos.com/graphing.

Be sure to title the graph as your first and last name. Also, label and number the x-axis

and y-axis appropriately so that the graph matches the calculated values from above.

Your graph will only be a part of a parabola because the domain of this quadratic

function is [0, 600]. (20 points)

Insert your graph below:

Page 6 of 6

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