A real estate office handles a 80-unit apartment complex. When the rent is $560 per month, all units are occupied. For each $45 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

$2,090 should be charged as rent to obtain maximum profit.

Explanation:

Let's assume x is the number of occupied apartment.

Therefore, the total rent the company is getting can be represented as;

{(560 + 45(80-x)}x-50x

Y=560x + 3600x - 45x^2 - 50x

Y=4110x - 45x^2

Y^'=(4110x - 45x^2)^'

Y=4110 - 90x

Y=0

4110-90x = 0

90x = 4110

x = 45.67

Rent is therefore;

560 + (80 - 46)45

=560 + 1530

=$2,090

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