Boise Lumber has decided to enter the lucrative prefabricated housing business.
ID: 3196143 • 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 Luxury Model 10,000 200 300 $5,000 Deluxe Model Material Factory Labor (hr) On-Site Labor (hr Profit 000$8,000 240 180 220 210 $3,400 000 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 rescarch has confirmed that there should be no problems with sales.) standard model deluxe model luxury model houses houses housesExplanation / Answer
x -standard
y -deluxe
z- luxury
Maximize Z = 3400x + 4000y + 5000z subject to,
6000x + 8000y + 10000z <= 8200000
240x + 220y + 200z <= 212000
180x + 210y + 300z <= 234000
this can be solved using Excel, LINDO , simplex method etc
Optimal Solution: Z = 4180000; x = 200, y = 400, z = 380
for simplex
Tableau #1
x y z s1 s2 s3 z
6000 8000 10000 1 0 0 0 8200000
240 220 200 0 1 0 0 212000
180 210 300 0 0 1 0 234000
-3400 -4000 -5000 0 0 0 1 0
Tableau #2
x y z s1 s2 s3 z
0 1000 0 1 0 -33.3333 0 400000
120 80 0 0 1 -0.666667 0 56000
0.6 0.7 1 0 0 0.00333333 0 780
-400 -500 0 0 0 16.6667 1 3900000
Tableau #3
x y z s1 s2 s3 z
0 1 0 0.001 0 -0.0333333 0 400
120 0 0 -0.08 1 2 0 24000
0.6 0 1 -0.0007 0 0.0266667 0 500
-400 0 0 0.5 0 0 1 4100000
Tableau #4
x y z s1 s2 s3 z
0 1 0 0.001 0 -0.0333333 0 400
1 0 0 -0.000666667 0.00833333 0.0166667 0 200
0 0 1 -0.0003 -0.005 0.0166667 0 380
0 0 0 0.233333 3.33333 6.66667 1 4180000