Boise Lumber has decided to enter the lucrative prefabricated housing business.
ID: 3216444 • 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. Standard Model Deluxe Model Luxury Model 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 budgeted for the building material; the number of labor-hours available for work in the factory is not to exceed 215,000 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. standard model Incorrect: Your answer is incorrect. houses deluxe model Incorrect: Your answer is incorrect. houses luxury model Incorrect: Your answer is incorrect. houses
Explanation / Answer
Let the number of standard houses be x
Let the number of deluxe houses be y
Let the number of luxury houses be z
Maximize P = 3400x + 4000y + 5000z
Constraints:
6000x + 8000y + 10000z <= 8200000 [Dollar amount building material constraint]
240x + 220y + 200z <= 215000 [Factory labour hour]
180x + 210y + 300z <= 240000 [site labour hours]
x>0,y>0,z>0
Solving the linear equation by finding the maxima
The maxima exists at x=325,y=200 and z=465
Maximum Profit = 3400(325) + 4000(200) + 5000(465) = $4230000