Problem 2 A rectangular pen is to be built with 1200 m of fencing. The pen is to be divided into three parts using two parallel partitions a) Find the maximum possible area of the pen. b) Explain how the maximum area would change if each side of the pen had to be at least 180 m long . Problem 3 A showroom for a car dealership is to be built in the shape of a rectangle with brick on the back and sides , and glass on the front . The floor of the showroom is to have an area of 500 . If a brick wall costs $1200 fm while a glass wall costs $600 fm, what dimensions would minimize the cost of the showroom ? Problem 4 A Norman window has the shape of a rectangle with a semicircular top. a) For a given perimeter , find the ratio of the height to radius that will maximize the window's area. b) Assume that the semicircular portion of the perimeter is three times as costly to built per meter as the straight edges . For a given area , what ratio of height to radius would minimize cost? Problem 5 A Cylindrical can is to have a volume of 1 L