The function #P(x)=-750x^2 + 15, 000x# models the profit, P, in dollars for a company that manufactures large computers, where x is the number of computers produced. For which value of x will the company make a maximum profit?

1 Answer
Binayaka C.
Nov 29, 2016

Producing #10# computers company will earn maximum profit of #75000#.

Explanation:

This is a quadratic equation. #P(x)=-750x^2+15000x ;# here #a= -750 , b=15000 , c=0 ; a <0# The curve is of a parabola opening downwards. So vertex is the maximum pt in the curve. So maximum profit is at #x=-b/(2a) or x= -15000/(-2*750)=15000/1500=10 ; x=10 ; P(x)= -750*10^2+15000*10=-75000+150000=75000#

Producing #10# computers company will earn maximum profit of #75000#.[Ans]

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