Alice gardener wants to build a rectangular enclosure with a dividing fence in the middle of the rectangle. On one side, she plans to put some goats, on the other side she wants to raise some vegetables. The fence along the outside of the rectangle costs $3 per foot, but the dividing fence costs $12 per foot. (a) Alice decides to spend $240 on the fencing, what is the maximum area she can enclose? Justify your answer.

(b) If Alice decided she wants to enclose 300 square feet, what is the minimum cost?