Answers should be given in exact form. Justify each answer by providing

supporting details utilizing calculus methods. Answers with incorrect or incomplete

justification may not receive full credit.

1. A fence is to be built in a large field to enclose a rectangular region of

14,400 square meters. One side of the region is bounded by an existing

fence; no fence is needed there. Material for the fence costs $2 per meter

for the two ends, and $4 per meter for the side opposite the existing fence.

Find the cost of the least expensive fence.