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24 February, 11:44

Demand for an electric fan is related to its selling price p (in dollars) by the equation n = 3680 - 80 p where n is the number of fans that can be sold per month at a price p. Find the selling price that will maximize the revenue.

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  1. 24 February, 12:02
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    The price of $23 will maximize the total revenue.

    Explanation:

    Revenue is a function of price multiplied by quantity. Thus, the equation for revenue is,

    Let p be the price.

    Revenue = (3680 - 80p) * p

    Revenue = 3680p - 80p²

    To find the price that will maximize the revenue, we need to take the derivative of this equation as derivative tell us about change.

    Taking derivative,

    d/dp = 1 * 3680 - 2 * 80p

    0 = 3680 - 160p

    160p = 3680

    p = 3680 / 160

    p = 23

    So, at price p=$23, the total revenue will be maximized.
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