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3 January, 22:56

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 132 in. Find the dimensions of a rectangular package that has a square cross section and largest volume that may be sent by priority mail. Hint: The length plus the girth is 4x + l.

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  1. 4 January, 00:35
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    v = 11264 in^3

    Step-by-step explanation:

    4 x + l = 132

    l=132 - 4 x

    v = h x^ 2

    = x ^ 2 (132 - 4 x)

    = 132 x ^ 2 - 4 x^3

    = 4 (33 x^2 - x ^3)

    d v/d x = 4 (66 x - 3 x^2)

    = 12 x (22 - x)

    d v/d x = 0

    when x = 0 or 22

    So

    h = 132 - 4 * 22 = 44

    So if the package is 44*16*16

    v = 11264 in^3

    So 4 x+l > = 132 But it should be minimum if 4 x+l contain smaller value
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