Boise Lumber has decided to enter the lucrative prefabricated housing business.

Question

Boise Lumber has decided to enter the lucrative prefabricated housing business. Initially, it plans to offer three models standard, deluxe, and luxury. Each house is prefabricated and partially assembled in the factory, and the final assembly is completed on site. The dollar amount of building material required, the amount of labor required in the factory for prefabrication and partial assembly, the amount of on-site labor required, and the profit per unit are as follows Material Factory Labor (hr) On-Site Labor (hr) Profit Standard Model $6,000 240 180 $3,400 Deluxe Model $8,000 220 210 $4,000 Luxury Model $10,000 200 300 $5,000 For the first year's production, a sum of $8,200,000 is budgeted for the building material; the number of labor-hours available for work in the factory (for prefabrication and partial assembly) is not to exceed 212,000 hr; and the amount of labor for on-site work is to be less than or equal to 234,000 labor-hours. Determine how many houses of each type Boise should produce to maximize its profit from this new venture. (Market research has confirmed that there should be no problems with sales.) standard model 200 deluxe model 400 houses houses X houses luxury model 395

Explanation / Answer

This problem can be solved by using linear programming

Given problem can be formulated as LPP as shown below,

Let x, y and z be number of houses to be built of each type standard, deluxe and luxary respectively

Maximize Z = 3400x + 4000y + 5000z subject to,
6000x + 8000y + 10000z <= 8200000
240x + 220y + 200z <= 212000
180x + 210y + 300z <= 234000

Optimal Solution: z = 4180000; x = 200, y = 400, z = 380

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