A real 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)
