A real estate office manages 50 apartments in a downtown building. When the rent is $900 per month, all the units are occupied. For ever $25 increase in rent, one unit becomes vacant. On average, all units require $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits.
2. The attempt at a solution
Total = (Number of apartments)(Monthly rent)
T = (50 + 25x)(900-75x)
T = (45000 - 3750x + 22500x - 1875x2)
T = -1875x2 + 18750x + 45000
T' = -3750x + 18750
0 = -3750x + 18750
3750x = 18750
x = 5
I'm not sure if I'm actually doing this correctly or if I'm getting anywhere that's actually correct.
The answer is: $1100 or $1125.
Suggestions are welcome and helpful!