Question

A page should have perimeter of 42 inches. The printing area within the page would be determined by top and bottom margins of 1 inch from each side, and the left and right margins of 1.5 inches from each side. What should be the overall dimensions of the page in order to maximize the printing area?

Answer 1

let the width of the page be x inches
and its length be y inches

2(x+y) = 42
x+y = 21
y = 21-x

width of printed area = x-3
length of printed area = y-2

area = (x-3)(y-2)
= (x-3)(21-x - 2)
= (x-3)(19-x)
= -x^2 + 22x - 57

d(area)/dx = -2x + 22
= 0 for a max of area
2x=22
x = 11
then y = 21-11 = 10

page should be 11 inches wide and 10 inches long