Your College is building a new running track. It is to be the perimeter of a region obtained by putting two semicircles on the ends of a rectangle. However, the administration decides they’d also like...

Your College is building a new running track. It is to be the perimeter of a region obtained by putting two semicircles on the ends of a rectangle. However, the administration decides they’d also like to have an outdoor pool in the rectangular portion of the area surrounded by the track. Assume the track is to be 440 yards long.

(a) Determine the necessary dimensions to build the track in order to maximize the area of the pool. (Assume the edges of the pool are exactly along the straight line part of the track.) State your conclusion clearly.

(b) Could you use the Single Critical Point theorem to justify you’ve found the maximum? If so, do it. If not, why not.

(c) Could you use the Closed Interval Method? If so, do it. If not, why not.