1. ## optimization problem.

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, all units require $75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits? I did it like this: let x represents the number of increase or decrease in rent and apartment, then I got the equation: Revenue(x)= [(900+25x)(50-x)]-(50*75) but I know I must did something wrong... Can someone help me with this? 2. Originally Posted by Soul to soul 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, all units require$75 in maintenance and repairs each month. How much rent should the real estate office charge to maximize profits?

I did it like this: let x represents the number of increase or decrease in rent and apartment, then I got the equation:
Revenue(x)= [(900+25x)(50-x)]-(50*75)

but I know I must did something wrong... Can someone help me with this?
really close ...

$\displaystyle R(x) = (900+25x)(50-x)$

costs, $\displaystyle C = 50\cdot 75 = 3750$

profit ... $\displaystyle P(x) = R(x) - C = (900+25x)(50-x) - 3750$

now find the value of x that maximizes profit, P(x)