7) A certain window is in the shape of a rectangle surmounted by a semicircle. The rectangular glass is clear (not tinted). The semicircular glass is tinted and only lets in half as much light per unit area as the clear glass. The perimeter is fixed at P units. Find the dimensions of the window that will admit the most light. Assume the base of the rectangular glass is 2r inches and the height of the rectangular glass is h inches. See diagram below. Hint: The radius r that maximizes the amount of light will be in terms of P, the perimeter. + J 2r The dimensions that let in the most light are: and h =