A rectangular page is to contain 8 square inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide. Find the dimensions of the page that will minimize the amount of paper used. (Let x represent the width of the page and let y represent the height.)

Question

Steve · Answer

So, let the width of print be x, and the height be y.

xy = 8
y = 8/x

That means that the area of the page is

a = (x+2)(y+4) = (x+2)(8/x+4) = 4x+16+16/x

da/dx = 4-16/x^2

So, find where da/dx=0 for minimum area.

Note that I used x and y for the dimensions of the printed part. It just means that the equation will be different, but the answer will be the same.