In Chapter 3, we saw that the profit, P(x), generated after producing and selling x

Chapter 8, Problem 70

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In Chapter 3, we saw that 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, respectively. Use these functions to solve Exercises 6970.Virtual Fido is a company that makes electronic virtualpets. The fixed weekly cost is $3000, and variable costs foreach pet are $20.a. Let x represent the number of virtual pets made andsold each week. Write the weekly cost function, C, forVirtual Fido.b. The function R(x) = -x2 + 1000x describes themoney that Virtual Fido takes in each week from thesale of x virtual pets. Use this revenue function andthe cost function from part (a) to write the weekly profitfunction, P.c. Use the profit function to determine the number ofvirtual pets that should be made and sold each weekto maximize profit. What is the maximum weeklyprofit?