Answer to Question #129560 in Calculus for Tommy

Question #129560
The profit (in thousands of dollar) of a company is given by P(x) = 500 + 100x -5x^2 , where x is the amount (in thousands) the company spends on adverting, The amount , x, that the company spend to maximize the profit is?
1
Expert's answer
2020-08-14T17:52:02-0400

"P(x)=500+100x-5x^2" .

"\\frac{dP}{dx}=0\\to100-10x=0\\to x=10."

"\\frac{d^2P}{dx^2}=-10<0."

Thus, the function of profit has its maximum at "x=10."

"P(10)=500+100*10-5*10^2=1000."


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