A real estate office handles 50 apartment unists. When the rent is $720 a month, all units are occupied. When the rent is increased by $40, one unit becomes vacant. Each occupied unit requires an average of $48 a month for maintenance. What rent should be charged to obtain max. profit.

My work:P(profit); C(cost); R(revenue); p(x)[price per unit];

$\displaystyle P(x)=R(x)-C(x)$

so; $\displaystyle C(x)=(50-x)(48)$ and $\displaystyle R(x)=(720+40x)(50-x)$

$\displaystyle P(x)=-40x^2+1328x+constant$

$\displaystyle P'(x)=-80x+1328$ and $\displaystyle P'(x)=0///when///x=16.6$

And since I get x=16.6 I get a bit of doubt but then I test x=16 and x=17 on P(x) and get that to maximum profit x=17; so $1,400 should be charged.

Thanks for your time.