A real estate company owns 218 apartment units These apartme

A real estate company owns 218 apartment units. These apartment units are fully occupied whrn the rent is $940 per month. The company found out that for each $25 increase in rent, 5 apartment units will become unoccupied. What amount of that rent should be implemented in order to have a total earning of $205,920?

Solution

There are 218 apartments and rent is $940 per month

each $25 increase in rent, 5 apartment units will become unoccupied

Let say there are x increasse of $25 which would lead to rent = $(940 - 25x)

No. of units unoccupied = 5x

So, occupied = 218 -5x

Total earnings = no. of apartments*rent per month = (218- 5x)(940 - 25x) = 205920

204920 - 5450x -4700x +125x^2 = 205920

125x^2 -10150x -1000 =0

x = 81.3 and x = - 0.1

Rent for which total earning is $205,920 = 940 -25*81.3 = -ve .We neglect this value

for x= -0.1 Rent = 940 - 25(-0.1) = $942.5

Rent = $ 942.5 for total earning of $205,920