Asked by Godfrey
A graphic designer is asked to create a movie poster with a 65 square-inch photo surrounded by a 3 inch border at the top and bottom and a 2 inch border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?
Answers
Answered by
oobleck
if the printed area is x inches wide and y inches high then we have the paper area is
a = (y+6)(x+4)
since xy=65, that gives us
a = (65/x + 6)(x+4) = 6x+89 + 260/x
a has a minimum when da/dx = 0, so we want
6 - 360/x^2 = 0
x = √(130/3)
y = √390/2
and the paper area is
a = (√390/2+6)(√(130/3)+4) = 89+4√390
a = (y+6)(x+4)
since xy=65, that gives us
a = (65/x + 6)(x+4) = 6x+89 + 260/x
a has a minimum when da/dx = 0, so we want
6 - 360/x^2 = 0
x = √(130/3)
y = √390/2
and the paper area is
a = (√390/2+6)(√(130/3)+4) = 89+4√390
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