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Math Help - business cal

  1. #1
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    business cal

    i am at a road block with this problem and really need help plz

    A company manufactures and sells x air conditoners per month. the monthly cost and price-demand equations are
    C(x) = 180x + 20,000
    p = 220-0.001x 0<x<100,000

    how many air conditioners should the company manufacture each month to maximize its monthly profit??
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by almiller08 View Post
    i am at a road block with this problem and really need help plz

    A company manufactures and sells x air conditoners per month. the monthly cost and price-demand equations are
    C(x) = 180x + 20,000
    p = 220-0.001x 0<x<100,000

    how many air conditioners should the company manufacture each month to maximize its monthly profit??
    Profit is revenue minus costs so:

    Pr(x)=x\times p(x)-C(x)=220x-0.001x^2-180x-20000

    Which you maximise by taking its derivative with respect to x, setting that to zero and solving for x (the sales at which profit is a maximum).

    CB
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