Question

A rectangular page is designed to contain 64 square inches of print. the margins at the top and bottom of the page are each 1 inch deep. the margins on each side are 1 1/2 inches wide. what should the dimensions of the page be so that the least amount of paper is used.

Answer 1

Let A be the area of paper, x be the width of the printed area, and y be the height of the printed area. A = (x + 2(1.5))(y + 2(1)) and xy = 64 A = (x + 3)(64/x + 2) A = 70 + 192/x + 2x dA/dx = -192/x^2 + 2 = 0 96 = x^2 x = 4sqrt(6) x + 3 ≠12.8 in. y = 64/[4sqrt(6)] = 8sqrt(6)/3 y + 2 ≠8.53 in.