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Math Help - optimization problem.

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by Soul to soul View Post
    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 ...

    R(x) = (900+25x)(50-x)

    costs, C = 50\cdot 75 = 3750

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

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