# You are designing a rectangular poster to contain 50 in^2 of printing with a 4-in. margin at the top and bottom and a 2-in margin at each side. What overall dimensions will minimize the amount of paper used?

##### 1 Answer

Jan 19, 2016

18" x 9"

#### Explanation:

Let the paper size be x inches in length and y inches in width.

the length of the printed space would be x-8 inches and width would be y-4 inches. Print area would thus be (x-8)(y-4)= 50.

From this

Also from the same equation on simplifying, it is xy-8y-4x+32=50.

Since the area of the paper of size x inches by y inches is xy, let it be denoted as A. Thus

A-8y-4x=18 Or A= 8y+4x+18

x-8=10

x=18, hence y=

Dimension of minimum paper size would be 18 inches by 9 inches.