A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom.

Question

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom. Find the dimensions of the poster with the largest printed area

Answer 1

I interpret this to mean that the printed area plus the margins must be 100 in^2., i.e. LW=100

The printed area A=(L-2)(W-4)

Substitute W=100/L.

This gives a quadratic to be minimized: 4L²-108L+200.

The derivative is 8L-108.

You fill in the derivation of the quadratic and finish the problem from here.