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 12 lots, 47,500 labor-hours, and $3,413,000 available for the contractor's use.
(a) Building how many of each type of house will maximize his profit?
(b) What is the maximum possible profit?

Involve three variables. Solve them with the simplex method, Excel, or some other technology.

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