Boise Lumber has decided to enter the lucrative prefabricated housing business.
ID: 3196446 • Letter: B
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 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 240,000 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 deluxe model houses houses houses luxury modelExplanation / Answer
Variables
Optimal number of Standard, Deluxe and Luxury houses are S, D and L
Constraints
1. S, D and L are non-negative integers
2. total building material cost : 6000S + 8000D + 10000L <= 8,200,000
3. Factory labors : 240S + 220D + 200L <= 212000
4. On-site labors : 180S + 210D + 300L <= 240000
Objective
Maximize profit: 3400S + 4000D + 5000L
Solution
using excel solver
answer,
standard model 300
Deluxe model 200
Luxury model : 480
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Standard Deluxe Luxury Total Constraint Optimal no. 300 200 480 per house Material 6000 8000 10000 Factory labor 240 220 200 On-site labor 180 210 300 Profit 3400 4000 5000 total Material 1,800,000 1,600,000 4,800,000 8,200,000 - Factory labor 72,000 44,000 96,000 212,000 - On-site labor 54,000 42,000 144,000 240,000 - Profit 1,020,000 800,000 2,400,000 4,220,000