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First Letter of Your Last Name
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Possible values for b
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A-F
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$4,000 to $4,500
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G-L
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$4,501 to $5,000
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M-R
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$5,001 to $5,500
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S-Z
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$5,501 to $6,000
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1. Based on the first letter of your lastname, choose a value for your fixed cost, b. Use your chosen value for b to write your cost function, C(x). Then, useP(x)=R(x)-C(x)to write your simplifiedprofit function. Show all of thework details.
2. Using the vertex formula, where x=-b/(2a), at how manydownloads would your company achieve a maximum profit? How much is this maximum profit? Show all of the work details.
3. How many downloads would giveyou a profit of $30,000the next month?Show all of the work details.
(Hint: Let the profit function be equal to $30,000, and solve for x using the quadratic formula. Because the domain of the profit function is [0,600], be sure that the value of x is between 0 and 600.)
4. Complete the following table by calculating the profit for each number of downloads. Show all of the work details for x=50 and x=200only.)
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x, Number of Downloads
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P(x), Profit in U.S.Dollars
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20
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$ ?
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50
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$ ?
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100
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$ ?
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200
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$ ?
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300
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$ ?
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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].
6. Do you think thatdeveloping a mathematical model of a profit function,such as the one in this assignment,can helpa company understand its start-up dynamics?Explain the reasoning that led to your conclusion.
Attachment:- Submission Assignment.rar