Question

A real estate office handles a 80-unit apartment complex. When the rent is $550 per month, all units are occupied. For each $25 increase in rent, however, an average of one unit becomes vacant. Each occupied unit requires an average of $50 per month for service and repairs. What rent should be charged to obtain a maximum profit

Answer 1

The real estate should charge $1,300 to obtain maximum profit.

Step-by-step explanation:

We can make K to represent the number of unit apartment occupied.

This means that the total rent the real estate office is getting can be denoted by;

{(550 + 25(80 - K)} K - 50K

Maximizing the above equation, we have;

y = 550K + 2,000K - 25K^2 - 50K

Collect like terms

= 2,500K - 25K^2

y' = (2,500K - 25K^2)' = 2,500 - 50K

y = 0

2,500 - 50K = 0

2,500 = 50K

K= 50

Rent is therefore;

Rent = 550 + (80 - K)25, where K is 50

= 550 + (80 - 50)25

= 550 + (30)25

= 550 + 750

= $1,300