Expert: Sherman D. - 10/4/2004

Question
Student editors are designing the yearbook so that each rectangular page will have a perimeter of 40 inches.The printer advises the student editors that each page must have a margin of 1 and a half inches on the bottom and 1 inch on the other 3 sides.What must be the dimensions of the page if the printed area is to be as great as possible?The answer is w=9.75in.,h=10.25in.But I can't get it. Please explain the steps to get there.Thank you.

Answer
40 = 2(L + W)
20 = L + W

(L + 1.5 + 1) + (W + 1 + 1) = 20
L + 2.5 + W + 2 = 20
L + W + 4.5 = 20
L + W = 15.5
W = -L + 15.5

A = LW
A = L(-L + 15.5)
A = -L^2 + 15.5L

Using the formula
L = -b/(2a), in order to find the maximum.
L = (-15.5)/(-2)
L = 7.75

W = -(7.75) + 15.5
W = -7.75 + 15.5
W = 7.75

Now to find the true dimensions, use this

L + 1.5 + 1 = L + 2.5
7.75 + 2.5 = 10.25

W + 1 + 1 = W + 2
7.75 + 2 = 9.75

So the answer is

W = 9.75 inches
L = H = 10.25 inches

I used L instead of H.