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13 November, 07:55

Find two numbers x and y such that their sum is 60 and x2y is maximized.

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  1. 13 November, 08:02
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    X + y = 60

    P = x^2 y

    From first equation y = 60 - x

    P = x^2 (60 - x)

    P = 60x^2 - x^3

    Finding the derivative of P and equating to zero:-

    P' = 120x - 3x^2 = 0

    -3x (x - 40) = 0

    x = 40

    This makes y = 20

    So maximum values of x^2y = 40^2 * 20 = 32,000.
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