An apartment complex in Johannesburg has 90 units. When the monthly rent is $500 per unit, all units are rented. It is believed that for each $10 increase in rent, one apartment unit will become vacant.

Question

An apartment complex in Johannesburg has 90 units. When the monthly rent is $500 per unit, all units are rented. It is believed that for each $10 increase in rent, one apartment unit will become vacant.

The rent of $?rands maximizes the total revenue of the apartment complex ( Hint: The rent is a positive integer).

Answer 1

R = revenue , v = number of vacant apartments

R = (90 - v) (500 + 10 v) = 45000 + 400 v - 10 v^2

the max is on the axis of symmetry of the parabola

vmax = -400 / (2 * -10)

looks like 20 vacancies maximizes revenue