# 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?

Producing $10$ computers company will earn maximum profit of $75000$.
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]