A printer needs to make a poster that will have a total area of 200 in^2 and will have 1- inch margins on the sides,

Question

A printer needs to make a poster that will have a total area of 200 in^2 and will have 1- inch margins on the sides, a 2-inch margin on the top and a 1.5-inch margin on the bottom as shown in Figure 14. What dimensions will give the largest printed area? (approximate your answer to 4 decimal places.)

Answer 1

Width * Height = area. The width has 2 added for the margins. The height has 3.5 added for the margins.

w is width of the full poster.

h is height of the full poster = 200/w

w of the printed area = w-2 (subtract the margins).

h of the printed area = 200/w - 3.5 (subtract the margins top and bottom)

Printed Area = A = (w-2)(200/w - 3.5) = 200 - 400/w - 3.5w + 7 = -3.5w -400/w + 207

A' = -3.5 -400/w^2 = 0

-3.5w^2 -400 = 0

w^2 = 400/3.5

w = sqrt (400/3.5) = 10.6904

Height = 200/sqrt (400/3.5) = 18.7083