1. [10 marks] A Norman window has the shape of a rectangle surmounted by a semicircle. Given some perimeter of the window, we want to find the dimensions of the window so that the greatest possible amount of light is admitted. (a) Define appropriate variables and write expressions for the perimeter and area of the window. Recall: The circumference of a circle of radius r is 2mr. (b) If the perimeter of the window is 30 ft, find the dimensions of the window (to 1 decimal place) that will admit the greatest amount of light possible. Justify your answer completely. [Hint: Use either the first or second derivative test to justify your answer.]