Problems 45-48 involve three variables. Solve them with the simplex method, Excel, or some other technology.
Construction 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?
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 |
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