A contractor has a budget of $1,600 to build a rectangular enclosure. Two of the walls of the enclosure measurex

xmetres, and two of them measurey

ymetres. The standard cost to build one metre of wall is $40/m (forty dollars per metre). However, one of the walls mesuringx

xis a retaining wall, costing three times as much to build per metre than a regular wall. Your goal is to find the values ofx

xandy

yto maximise the area of the enclosure.

For full marks, your answer should contain (at least)

1. A formula relatingx
2. xandy
3. y
4. The formula for area in terms of bothx
5. xandy
6. y
7. The formula for area in terms ofx
8. xonly
9. The correct derivative to solve the problem
10. The correct critical point(s)
11. Correct use of the first derivative test
12. The optimal values ofx
13. xandy
14. y.