Calculus

A graphic designer is asked to create a movie poster with a 128 in^2 photo surrounded by a 4 in border at the top and bottoms and a 2 in border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?

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  1. let the width of the photo be x in
    then the length of the photo is 128/x in

    width of poster = x+8
    length of poster = 128/x + 8

    Area = (x+8)(128/x + 8)
    = 128 + 8x + 1024/x + 64
    d(area) = 8 - 1024/x^2
    = 0 for a min of area

    8 = 1024/x
    8x^2 = 1024
    x^2 =128
    x = √128 = 8√2

    carry on

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