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Math Help - Optimization of Revenue

  1. #1
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    Optimization of Revenue

    The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 490 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. What rent should the manager charge to maximize revenue?
    Ok for this I have set up the following:

    My webwork says I'm wrong so can someone help me identify what I did wrong?
    Thanks

    R(x) = (80-x)(490+7x)
    dR/dx = -(490 + 7x) + 7(80-x)
    0 = -490 - 7x - 7x + 560
    14x= 70
    x= 70/14

    Now I did (490 + 7(70/14))
    and got 520 please help
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  2. #2
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    Re: Optimization of Revenue

    Quote Originally Posted by habibixox View Post
    The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 490 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 7 dollar increase in rent. Similarly, one additional unit will be occupied for each 7 dollar decrease in rent. What rent should the manager charge to maximize revenue?
    Ok for this I have set up the following:

    My webwork says I'm wrong so can someone help me identify what I did wrong?
    Thanks

    R(x) = (80-x)(490+7x)
    dR/dx = -(490 + 7x) + 7(80-x)
    0 = -490 - 7x - 7x + 560
    14x= 70
    x= 70/14

    Now I did (490 + 7(70/14)) = 490 + 35 = 525
    and got 520
    ...
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