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## 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 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 - 1875x

^{2})

T = -1875x

^{2}+ 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!

Thanks!

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