optimization

Optimization Suppose you are helping build a house, and you have framed and cut a hole for a circular window of radius 12 inches. However, when it comes time to buy the actual window, you find out that circular windows cost 4 times as much as rectangular windows, which puts you over budget. (a) (5 points) Find the dimensions of the rectangular window inscribed in the circular hole that will maximize the amount of light that is let in. What area will your window have? Begin by sketching the window. (b) (5 points) Suppose instead on a separate project you are asked to build a window where a rect- angle is the base, and the top is a semicircle. If there are 16 meters of framing materials, what must the dimensions of the window be to let in the most light? What area will your window have? Begin by sketching the window