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

Question

A rectangular poster is to contain 288 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

Let t=length of the printed area and s=the width of the printed area.

ts=288 and

A=(t+4)(s+2) is the area of the poster to be minimized.

Substitute s=288/t into the equation for A.

Set dA/dt=0 and solve for t. Be careful with the differentiation!

You should get t=24 and s=12.