1. Checking answer for maximized profit.

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];

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

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

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

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

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.