A page of 150 square inches is to have margins of 1 inch on either side and 1 1/2 inches at the top and bottom, as in the diagram. Find the dimensions of the page that maximize the print area.

Answer 1

If the page has dimensions x and y, then we know

xy=150

Since it has margins all around, we want to maximize the print area

p = (x-2)(y-3) = (x-2)(150/x-3) = 156 - 3x - 300/x
dp/dx=0 when x=10
So, a 10 by 15 page has maximum print area.

Answer 2

12X18