A handbill is to contain 98 square inches of printed material, with 4-inch margins at the top and bottom and 2-inch margins on each side. What dimensions for the handbill would use the least amount of paper?
A) 10 inches by 19 inches
B) 5 inches by 24 inches
C) 11 inches by 22 inches
D) 16 inches by 25 inches

Question

Quizplus · Accepted Answer

We need to find the dimensions that minimize the amount of paper used. Let the width of the printed portion be x inches. Then the height of the printed portion would be 98/x inches. Adding the margins, the total width would be x+4 inches and the total height would be 98/x+4 inches. Thus, the total area of the handbill would be:

A(x) = (x+4) * (98/x+4)

To minimize the amount of paper used, we need to find the minimum of A(x). Taking the derivative and setting it to zero, we get:

A'(x) = -98/(x+4)^2 + 1 = 0

Solving for x, we get x=11. Plugging this back into A(x), we get A(11) = 242 square inches, which is the smallest area possible. Therefore, the dimensions that would use the least amount of paper are 11 inches by 22 inches (choice C).

A Handbill Is to Contain 98 Square Inches of Printed