What should the dimensions of the poster be so that the least amount of poster is used?

Question

A rectangular poster is to contain 882 square inches of print. The margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the poster be so that the least amount of poster is used?

Answer 1

Draw a figure!

Let x be the width of print space and y the height.

xy=882 => y=882/x

The area of the poster A = (x+2)(y+4)

Substitute for y in the area expression.

Differentiate A with respect to x and set that derivative = 0.

Solve this equation for x, get y and don't forget to add the margins in your answer.