This document provides solutions to three optimization problems involving rectangular advertisements or windows.
The first problem minimizes the total area of an advertisement given a fixed printed area, finding the dimensions are a 4.6 inch square printed region within a 6.6 by 6.6 inch advertisement.
The second problem maximizes the printed area of an advertisement given a fixed total area of 120 square inches, determining the optimal dimensions are a 4.5 by 6.5 inch advertisement.
The third problem maximizes the area of a window with a semicircular top and rectangular body given a fixed amount of trim, concluding the optimal dimensions are a 2 by 4 inch rectangle beneath a semicircle.