The problem below involves three variables. Solve it with the simplex method, Excel, or some other technology. A contractor builds three types of houses: the Aries, the Belfair, and the Wexford. Each house requires one lot, and the following table gives the number of labor-hours and the amount of capital needed for each type of house, as well as the profit on the sale of each house. There are 14 lots, 56,100 labor-hours, and $3,963,800 available for the contractor's use.

		Aries		Belfair		Wexford
Labor-hours		3,000		3,700		5,000
Capital		$205,000		$279,600		$350,000
Profit		$20,000		$25,000		$30,000

(a) Building how many of each type of house will maximize his profit?

Aries	houses
Belfair	houses
Wexford	houses

(b) What is the maximum possible profit?