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.

Question

Amelie

Mathematics

1 June, 20:03

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.

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Yuliana Myers · 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 â‰ 12.8 in. y = 64/[4sqrt (6) ] = 8sqrt (6) / 3 y + 2 â‰ 8.53 in.