The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 396 dollars per month.

Question

The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 396 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 6 dollar increase in rent. Similarly, one additional unit will be occupied for each 6 dollar decrease in rent. What rent should the manager charge to maximize revenue? 

Answer 1

R(x) = (90 - x)(396 + 6x)

R(x) = 35640 + 144x - 6x²

R(x) is maximum at x = -144/(2)(-6) or 12

The manager should charge 396 + 12(6) dollars per unit.