Week 2

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. Upload this modified Answer Form to the Intellipath Unit 2 Submission lesson. Make sure you submit your work in a modified MS Word document; hand-written work will not be accepted. If you need assistance, please contact your course instructor.

Suppose that you have a start-up company that develops and sells a gaming app for smartphones. You get to know the company’s financial performance by understanding your cost, revenue, and profit.

The monthly cost function (in U.S. dollars) of developing your app is, where is the cost, and is the number of app downloads. The $3 in the equation is called the variable cost per gaming app download, and b is called the fixed cost.

The monthly revenue function (in U.S. dollars), based on previous monthly sales, is modeled by the function ,

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

For each question, be sure to show all of your work details for full credit. Round all value answers to 2 decimal places.

1. Based on the first letter of your last name, choose a value for your fixed cost, b. Use your chosen value for to write your cost function, . Then, use to write your simplified profit function. Show all of the work details. (10 points)

Explain your answer here:

2. Using the vertex formula, where x = -b/(2a), at how many downloads would your company achieve a maximum profit? How much is this maximum profit? Show all of the work details. (20 points)

Explain your answer here:

3. How many downloads would give you a profit of $30,000 the next month? Show all of the work details. (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 is between 0 and 600.)

Explain your answer here:

4. Complete the following table by calculating the profit for each number of downloads. Show all of the work details for and only.) (20 points)

Explain your answer here:

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, online utilities like desmos.com, and many others.)

Insert both the function and the graph into the Word document containing your answers and work details. Be sure to label and number the axes appropriately so that the graph matches the chosen and calculated values from above. Your graph will only be a part of a parabola because the domain of this quadratic function is [0, 400]. (20 points)

Insert both your graph and function here:

6. Do you think that developing a mathematical model of a profit function, such as the one in this assignment, can help a company understand its start-up dynamics? Explain the reasoning that led to your conclusion. (10 points)

Explain your answer here:

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