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Math Help - Checking answer for maximized profit.

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    Checking answer for maximized profit.

    A real estate office handles 50 apartment unists. When the rent is $720 a month, all units are occupied. When the rent is increased by $40, one unit becomes vacant. Each occupied unit requires an average of $48 a month for maintenance. What rent should be charged to obtain max. profit.

    My work:P(profit); C(cost); R(revenue); p(x)[price per unit];

    P(x)=R(x)-C(x)

    so; C(x)=(50-x)(48) and R(x)=(720+40x)(50-x)

    P(x)=-40x^2+1328x+constant

    P'(x)=-80x+1328 and P'(x)=0///when///x=16.6

    And since I get x=16.6 I get a bit of doubt but then I test x=16 and x=17 on P(x) and get that to maximum profit x=17; so $1,400 should be charged.

    Thanks for your time.
    Last edited by Arturo_026; November 4th 2009 at 02:41 PM.
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