Rent to maximize profit with occupancy dropping per rent increase

[thomasrules]

Homework Statement

A Real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For every $25 increase in rent, one unit becomes vacant. On average, each unit requires $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits?

Homework Equations

The Attempt at a Solution

I really don't know how to go about this. what is the revenue? i mean obviously the price to rent x # of rooms rented. But yea...I really don't know

the Cost = 75x

 

[Tom1992]

get the profit function, which is the revenue minus the profit. then take the derivative and set it to zero to get your critical point, but don't forget to consider the interval for x, and show that you indeed get a maximum.