Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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●
Min
s.t.
0₁
0₁
0₁
+
Oak 01 =
Cherry C1-
0₂
Total Cost - $
0₂
0₂
+
03
02 =
C₂-
03
03
C₁
Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3
C₁
03 =
C3-
C₂
C₁
C₂
01, 02, 03, C1, C2, C3 2 0
C₂
c. If Cabinetmaker 1 has additional hours available, would the optimal solution change?
C3
C3
MANA
d. If Cabinetmaker 2 has additional hours available, would the optimal solution change?
C3
S
<l
S
|
|S|
I
1-1
b. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to
three decimal places, and for the total cost to two decimal places.
|
Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Hours avail. 1
Hours avail. 2
Hours avail, 3
Oak
Cherry
Transcribed Image Text:● Min s.t. 0₁ 0₁ 0₁ + Oak 01 = Cherry C1- 0₂ Total Cost - $ 0₂ 0₂ + 03 02 = C₂- 03 03 C₁ Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 C₁ 03 = C3- C₂ C₁ C₂ 01, 02, 03, C1, C2, C3 2 0 C₂ c. If Cabinetmaker 1 has additional hours available, would the optimal solution change? C3 C3 MANA d. If Cabinetmaker 2 has additional hours available, would the optimal solution change? C3 S <l S | |S| I 1-1 b. Solve the model formulated in part (a). What proportion of the oak cabinets and what proportion of the cherry cabinets should be assigned to each cabinetmaker? What is the total cost of completing both projects? If required, round your answers for the proportions to three decimal places, and for the total cost to two decimal places. | Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. Hours avail. 1 Hours avail. 2 Hours avail, 3 Oak Cherry
eBook
Problem 8-25 (Algorithmic)
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation.
For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are
shown here:
1
Hours required to complete all the oak cabinets
Hours required to complete all the cherry cabinets
Hours available
Cost per hour
C₁
Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3
50
61
35
$36
proportion of Oak cabinets assigned to cabinetmaker 1
proportion of Oak cabinets assigned to cabinetmaker 2
proportion of Oak cabinets assigned to cabinetmaker 3
proportion of Cherry cabinets assigned to cabinetmaker 1
C2 proportion of Cherry cabinets assigned to cabinetmaker 2
C-proportion of Cherry cabinets assigned to cabinetmaker 3
=
44
46
25
For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only
complete 35/50 0.7, or 70%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 35/61 -0.57, or 57%, of the cherry cabinets if it worked only on cherry cabinets.
a. Formulate a linear programming model that can be used to determine the proportion of the oak cabinets and the proportion of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects.
Let 01
O₂
03
$43
32
34
30
$56
Transcribed Image Text:eBook Problem 8-25 (Algorithmic) Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: 1 Hours required to complete all the oak cabinets Hours required to complete all the cherry cabinets Hours available Cost per hour C₁ Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 50 61 35 $36 proportion of Oak cabinets assigned to cabinetmaker 1 proportion of Oak cabinets assigned to cabinetmaker 2 proportion of Oak cabinets assigned to cabinetmaker 3 proportion of Cherry cabinets assigned to cabinetmaker 1 C2 proportion of Cherry cabinets assigned to cabinetmaker 2 C-proportion of Cherry cabinets assigned to cabinetmaker 3 = 44 46 25 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 35/50 0.7, or 70%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 35/61 -0.57, or 57%, of the cherry cabinets if it worked only on cherry cabinets. a. Formulate a linear programming model that can be used to determine the proportion of the oak cabinets and the proportion of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. Let 01 O₂ 03 $43 32 34 30 $56
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