Calculus

A graphic designer is asked to create a movie poster with a 162 in2 photo surrounded by a 4 in border at the top and bottom 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. If the photo's dimensions are
    width = x
    height = y
    xy = 162, so y = 162/x
    Then we have total poster area is
    a = (x+4)(y+8) = (x+4)(162/x + 8)
    find x such that da/dx = 0

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