A manufacturer has total cost (C)x= 2000+196x+3x^2 and the total revenue is R(X)

Question

A manufacturer has total cost (C)x= 2000+196x+3x^2 and the total revenue is R(X)= 500-X^2 where x units are manufactured per week. How many units should be manufactured for maximum profir? What is the max profit?

Explanation / Answer

Profit=Revenue-Total Cost Total cost (C)x= 2000+196x+3x^2 ==> Marginal cost=196+6x Total Revenue is R(X)= 500-X^2 ==>Marginal Revenue=2X For Maximum profit MC=MR ==> 196+6x=-2x Which is not possible because x cannot be negative. I guess the Function is not properly defined please check it out otherwise,Let me just tell you the steps equate MC=MR to get x and then put x in revenue function and cost function to get Total revenue and Total cost now substract the revenue and cost to get profit

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