Boise Lumber has decided to enter the lucrative prefabricatedhousing business. Initially, it plans to offer three models:standard, deluxe, and luxury. Each house is prefabricated andpartially assembled in the factory, and the final assembly iscompleted on site. The dollar amount of building material required,the amount of labor required in the factory for prefabrication andpartial assembly, the amount of on-site labor required, and theprofit per unit are as follows.
| StandardModel | DeluxeModel | LuxuryModel |
|---|
| Material | $6,000 | $8,000 | $10,000 |
|---|
| Factory Labor(hr) | 240 | 220 | 200 |
|---|
| On-Site Labor(hr) | 180 | 210 | 300 |
|---|
| Profit | $3,400 | $4,000 | $5,000 |
|---|
For the first year's production, a sum of $8,200,000 is budgetedfor the building material; the number of labor-hours available forwork in the factory (for prefabrication and partial assembly) isnot to exceed 215,000 hr; and the amount of labor for on-site workis to be less than or equal to 234,000 labor-hours. Determine howmany houses of each type Boise should produce to maximize itsprofit from this new venture. (Market research has confirmed thatthere should be no problems with sales.)
| standardmodel    | houses |
| deluxemodel    | houses |
| luxurymodel    | houses |
