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14 November, 07:49

A parcel delivery service will deliver a package only if the length plus the girth (distance around, taken perpendicular to the length) does not exceed 116 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.

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  1. 14 November, 08:14
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    14449 inches^3

    Step-by-step explanation:

    length+girth=116 inches

    w + 4x = 116

    volume=x^2*w

    w=116-4x

    V=x^2 * (116-4x)

    for max value, dv/dx=0

    dv/dx = 232x-12x^2

    232x-12x^2=0

    x=19.3333

    w=116-4 (19.33)

    =38.67

    V=19.33^2*38.67=14449 inches^3
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