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3 September, 02:53

According to postal regulations, a carton is classified as "oversized" if the sum of its height and girth (the perimeter of its base) exceeds 192 in. Find the dimensions of a carton (in inches) with square base that is not oversized and has maximum volume. (Enter the three dimensions as a comma-separated list.)

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  1. 3 September, 04:25
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    Square base dimension = 15 inches

    Maximum volume = 7200 inches^3

    Step-by-step explanation:

    V = x^2y ... eq 1

    Let the square base be x and the height y

    Oversize formular is given by

    Y + 4x = 92

    Y = 92 - 4x ... eq 2

    Put eq 2 into eq 1

    V = x^2 (92 - 4x^3)

    V = 92x^2 - 4x^3

    Using derivatives

    V = 184x - 12x^2

    V' = 0 = 184x - 12x^2

    X (184 - 12x)

    X=0

    X = 184/12 = 15.33 approximately 15 inches

    Maximum Volume = V = 92 (15) ^2 - 5 (15) ^3

    V = 92 (225) - 4 (3475)

    V = 20700 - 13500

    V = 7200 inches^3
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