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. 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 209,000 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 houses deluxe model houses luxury model houses

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 <= 209000

180x + 210y + 300z <= 234000

This problem can be solved using solver and below are the solutions

x = 175 (Standard Model)

y = 400 (Deluxe Model)

z = 395 (Luxury Model)

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