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 dimensi

Question

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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Liliana 22 hours 2021-10-12T10:39:50+00:00 1 Answer 0

Answers ( )

  1. Charlotte
    0
    2021-10-12T10:41:46+00:00

    Answer:

    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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