# 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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