11 1 points 06 Submissions Used My Notes Boise Lumber has de

11 1 points 0/6 Submissions Used My Notes 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 Factory Labor (hr) On-Site Labor (hr) Profit $6,000 240 180 $3,400 $8,000 220 210 $4,000 $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 is not to exceed 224,000 hr: and the amount of labor for on-site work is to be less than or equal to 243,000 labor-hours. Determine how many houses of each type Boise should produce to maximize its profit from this new venture. standard model deluxe model luxury model houses houses houses Submit Assignment Home My Assignments

Solution

Standard = s
Deluxe = d
Luxury = L

We have :
6000s + 8000d + 10000L = 8200000
Divide by 2000 all the way :
3s + 4d + 5L = 4100

Now, for factory labor :
240s + 220d + 200L = 224000
Divide by 20 :
12s + 11d + 10L = 11200

Now for on site labor :
180s + 210d + 300L = 243000
Divide by 30 :
6s + 7d + 10L = 8100

So, equations are L
3s + 4d + 5L = 4100
12s + 11d + 10L = 11200
6s + 7d + 10L = 8100

Solving them, we have :
s = 450
d = 100
L = 470