Areal estate company owns 180 apartments which are fully occupied when the rent is $300 per month. the company estimates that for each $10 increase in rent, five apartments will become unoccupied. what rent should be charged in order to obtain the largest gross income?

R = 660 - 2u rent = 390 - 2(units_rented)
g = r u gross income = units rented * rent/unit
= u (660 - 2u)
dg/du = 660 - 4u
= 0 at u = 165 find the stationary points by setting dg/du = 0
u = 165 is a relative max because d²g/du² < 0
r = 660 - 2(165) = 330
g(180) = 54000 check the boundaries
g(0) = 0
g(165) > g(180) > g(0)

$330