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?

Answer 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

Answer 2

13/8 by 576/13