You are designing a rectangular poster to contain 50 inches squared of printing with a 4 inch margin at the top and bottom; and a 2 inch margin at each side. What overall dimensions will minimize the amount of paper used?
(x − 8)(y − 4) = 50, so y = 4 + 50
x−8
. Then
A(x) = x
4 + 50
x − 8 x > 8.
A
0
(x) = 4 −
400
(x − 8)2
, so A
0
(x) = 0 gives x = 18. A
00(x) = 800
(x − 8)3
> 0
so the function is concave up, so x = 18 is the absolute minimum. When x = 18, y = 9.
