Question

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?

Answer 1

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

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

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

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

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