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Math Help - profit maximization

  1. #1
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    Smile profit maximization

    The monthly demand equation is p(x)=60-10^(-5)x where p is the price measured and x is the quanity/demand measured in kilowatt-hour.

    Currently the utility has fixed cost of 7000000 and marginal cost of $30.

    What is the profit maximization equation?
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  2. #2
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    Quote Originally Posted by boshbosh08 View Post
    The monthly demand equation is p(x)=60-10^(-5)x where p is the price measured and x is the quanity/demand measured in kilowatt-hour.

    Currently the utility has fixed cost of 7000000 and marginal cost of $30.

    What is the profit maximization equation?
    Have you calculated the profit itself? It is of course, 'price times quantity minus costs' (costs are fixed cost plus marginal cost times x). Since that function turns out to be a quadratic, you can find the maximum by completing the square and finding the vertex (highest point on the graph).
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