Calculus:Derivatives

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.