```Question 309414
The profit P(x), generated after producing and selling x units of a product is given by the function
P(x) = R(x) – C(x), where R and C are the revenue and cost functions.
Virtual Fido is a company that makes electronic virtual pets.
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The fixed weekly cost is \$3000, and variable costs for each pet are \$20.
Answer the following questions and show all work.
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a. Let x represent the number of virtual pets made and sold each week. Write the weekly cost function, C, for Virtual Fido.
C(x) = 3000+20x
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b. The function R(x) = -x^2 + 1000x describes the money that Virtual Fido takes in each week from the sale of x virtual pets.
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Use this revenue function and the cost function from part (a) to write the weekly profit function, P.
P(x) = -x^2+1000x -(3000+20x)
P(x) = -x^2 + 980x - 3000
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c. Use the profit function to determine the number of virtual pets that should be made and sold each week to maximize profit.
max occurs when x = -b/2a = -980/(2(-1)) = 490
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What is the maximum weekly profit? Show all work.
P(490) = -490^2 + 980*490 - 3000 = \$237,100
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Cheers,
Stan H.
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