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. The fixed weekly cost is $3000, and variable costs for each pet are $20.
Answer the following questions and show all work.
a. Let x represent the number of virtual pets made and sold each week. Write the weekly cost function, C, for Virtual Fido.
b. The function R(x) = -x2 + 1000x describes the money that Virtual Fido takes in each week from the sale of x virtual pets. Use this revenue function and the cost function from part (a) to write the weekly profit function, P.
c. Use the profit function to determine the number of virtual pets that should be made and sold each week to maximize profit. What is the maximum weekly profit? Show all work.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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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