A linear programming computer package is needed. 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. Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 42 30 Hours required to complete all the cherry cabinets 60 48 35 Hours available 40 30 35 Cost per hour $36 $42 $55 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets.

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A linear programming computer package is needed.
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.
Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3
Hours required to complete
all the oak cabinets
50
42
30
Hours required to complete
all the cherry cabinets
60
48
35
Hours available
40
30
35
Cost per hour
$36
$42
$55
For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all
the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus,
Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly,
Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets.
(a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the
percentage 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 = percentage of oak cabinets assigned to cabinetmaker 1, 02 =
percentage of cak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker
3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to
cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.)
Transcribed Image Text:A linear programming computer package is needed. 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. Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 42 30 Hours required to complete all the cherry cabinets 60 48 35 Hours available 40 30 35 Cost per hour $36 $42 $55 For example, Cabinetmaker 1 estimates it will take 50 hours to complete all the oak cabinets and 60 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 40 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 40/50 = 0.80, or 80%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 40/60 = 0.67, or 67%, of the cherry cabinets if it worked only on cherry cabinets. (a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage 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 = percentage of oak cabinets assigned to cabinetmaker 1, 02 = percentage of cak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker 3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.)
(a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the
percentage 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 = percentage of oak cabinets assigned to cabinetmaker 1, 02 =
percentage of oak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker
3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to
cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.)
Min 18000, + 176402- 16500, + 2160C, + 2016C, + 1925C,
s.t.
500, + 60C, s 40
hours available 1
420, + 48C, s 30
hours available 2
3003 + 35C3 s 35
hours available 3
0, +0,+03=1
oak
cherry
C+ Cz+ C3 =1
01, 02, 03, C1, C2, C3 2 0
Transcribed Image Text:(a) Formulate a linear programming model that can be used to determine the percentage of the oak cabinets and the percentage 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 = percentage of oak cabinets assigned to cabinetmaker 1, 02 = percentage of oak cabinets assigned to cabinetmaker 2, 03 = percentage of oak cabinets assigned to cabinetmaker 3, C1 = percentage of cherry cabinets assigned to cabinetmaker 1, C2 = percentage of cherry cabinets assigned to cabinetmaker 2, and C3 = percentage of cherry cabinets assigned to cabinetmaker 3.) Min 18000, + 176402- 16500, + 2160C, + 2016C, + 1925C, s.t. 500, + 60C, s 40 hours available 1 420, + 48C, s 30 hours available 2 3003 + 35C3 s 35 hours available 3 0, +0,+03=1 oak cherry C+ Cz+ C3 =1 01, 02, 03, C1, C2, C3 2 0
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