What rent should be charged to obtain a maximum profit?

Question

A real estate office handles a 40-unit apartment complex. When the rent is $530 per month, all units are occupied. For each $40 increase in rent, however, an average of one unit becomes vacant. Each occupied unit requires an average of $60 per month for service and repairs. What rent should be charged to obtain a maximum profit?

Answer 1

Income = (530 + 40x)(40 - x), where x represents each increase.

Put into vertex form to determine maximum and then add $60.

Answer 2

It sounds like you're doing good. $21,200/month. If you're paying $2400/month for maintenance; I hope that includes the fee to the janitors.