A rectangular page is to contain 97 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

Answer 1

Let the printed area have dimensions x and y. Then

xy = 97

Now you want the page to have minimum area A, so

A = (x+2)(y+2) = (x+2)(97/x + 2) = 2x+101+194/x
dA/dx = 2-194/x^2

So, find where dA/dx=0