Optimization Homework

You are going to build a christmas window and decorate it with lights around the outside. The window is rectangular with a semi-circular top. Around the semicircular part you will use extra special flashy lights that cost $3.50 per inch, whereas the lights around the rectangular part cost $2.00 per inch. If the area of the window needs to be 84 inches2, state, but do not solve, the underlying mathematical problem that needs to be solved so that the
total cost is minimized.