York Lane Bicycles (YLB) manufactures six models of Electric Scooters. Four e-Scooter models consist of product numbers and category letters, they are Model 101-A and 101-B, Model 202-A and 202-B. Other two models, Model 303 and Model 404 only include product numbers. Design, Cutting, Assembly and Testing are four major departments for producing e-Scooters before YLB ships them. Time requirements of e-Scooters will stay in each department are summarized in the following table: Product Model 101-A Model 101-B Model 202-A Model 202-B Model 303 Model 404 Design 2 3 4 5 2 1 Department (in hours) Cutting Assembly 3 2 4 5 1 3 2 2 1 4 3 3 Department Design Cutting Assembly Testing Unit profit for Model 101-B, Model 202-A and Model 303 are $34, $18, and $20, respectively. Unit profit for rest models is $15. The following table shows the production time available in each department. Capacity (in hours) 1100 Testing 5 1 4 1 1300 1400 1000 3 2 In addition, the minimum production level for Model 101-A, 101-B, 202-A, and 202-B are 40, 85, 35, and 30 units, respectively. For Model 303 and 404 are 50 and 70 units, respectively. The firm's overall objective is to manufacture the e-Scooter models in such quantities as to maximize total profits. Bob, a new production manager of YLB, wants to manufacture B category at least 150 units to satisfy the booming market. He also targets that the total number of Model 101 must be at least double as great as the total number of Model 202. Develop a Linear Programming Model that will tell YLB how many manufacturing quantities of six e- Scooter models they should produce. a) Define decision variable(s) b) Write the objective function. c) Write all constraints. The righthand-side values of the constraints must be constant values.
York Lane Bicycles (YLB) manufactures six models of Electric Scooters. Four e-Scooter models consist of product numbers and category letters, they are Model 101-A and 101-B, Model 202-A and 202-B. Other two models, Model 303 and Model 404 only include product numbers. Design, Cutting, Assembly and Testing are four major departments for producing e-Scooters before YLB ships them. Time requirements of e-Scooters will stay in each department are summarized in the following table: Product Model 101-A Model 101-B Model 202-A Model 202-B Model 303 Model 404 Design 2 3 4 5 2 1 Department (in hours) Cutting Assembly 3 2 4 5 1 3 2 2 1 4 3 3 Department Design Cutting Assembly Testing Unit profit for Model 101-B, Model 202-A and Model 303 are $34, $18, and $20, respectively. Unit profit for rest models is $15. The following table shows the production time available in each department. Capacity (in hours) 1100 Testing 5 1 4 1 1300 1400 1000 3 2 In addition, the minimum production level for Model 101-A, 101-B, 202-A, and 202-B are 40, 85, 35, and 30 units, respectively. For Model 303 and 404 are 50 and 70 units, respectively. The firm's overall objective is to manufacture the e-Scooter models in such quantities as to maximize total profits. Bob, a new production manager of YLB, wants to manufacture B category at least 150 units to satisfy the booming market. He also targets that the total number of Model 101 must be at least double as great as the total number of Model 202. Develop a Linear Programming Model that will tell YLB how many manufacturing quantities of six e- Scooter models they should produce. a) Define decision variable(s) b) Write the objective function. c) Write all constraints. The righthand-side values of the constraints must be constant values.
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
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Transcribed Image Text:York Lane Bicycles (YLB) manufactures six models of Electric Scooters. Four e-Scooter models
consist of product numbers and category letters, they are Model 101-A and 101-B, Model 202-A and
202-B. Other two models, Model 303 and Model 404 only include product numbers. Design, Cutting,
Assembly and Testing are four major departments for producing e-Scooters before YLB ships them.
Time requirements of e-Scooters will stay in each department are summarized in the following table:
Product
Model 101-A
Model 101-B
Model 202-A
Model 202-B
Model 303
Model 404
Design
2
3
4
5
2
1
Department (in hours)
Cutting Assembly
3
2
4
5
2
1
4
3
3
1
3
2
Department
Design
Cutting
Assembly
Testing
Testing
5
Capacity (in
hours)
1100
1300
1400
1000
1
4
Unit profit for Model 101-B, Model 202-A and Model 303 are $34, $18, and $20, respectively. Unit
profit for rest models is $15. The following table shows the production time available in each
department.
1
3
2
In addition, the minimum production level for Model 101-A, 101-B, 202-A, and 202-B are 40, 85, 35,
and 30 units, respectively. For Model 303 and 404 are 50 and 70 units, respectively.
The firm's overall objective is to manufacture the e-Scooter models in such quantities as to maximize
total profits. Bob, a new production manager of YLB, wants to manufacture B category at least 150
units to satisfy the booming market. He also targets that the total number of Model 101 must be at
least double as great as the total number of Model 202.
Develop a Linear Programming Model that will tell YLB how many manufacturing quantities of six e-
Scooter models they should produce.
a) Define decision variable(s)
b) Write the objective function.
c) Write all constraints. The righthand-side values of the constraints must be constant values.
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