MATH133 - Unit 2 Individual Project NAME (Required): My last name begins with \"F\" so use that for the assignment 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