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 13 lots, 47,800 labor-hours, and $3,398,400 available for the contractor use. Aries Belfair Wexford Labor-hours Capital Profit 3,000 $205,000 $20,000 3,700 $279,600 $25,000 5,000 $350,000 $30,000 (a) Building how many of each type of house will maximize his profit? Aries Belfair Wexford houses houses houses (b) What is the maximum possible profit?