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A company will be producing the same new product at two different factories, and then the product must be shipped to two warehouses. Factory 1 can send an unlimited amount by rail to warehouse 1 only, whereas factory 2 can send an unlimited amount by rail to warehouse 2 only. However, independent truckers can be used to ship up to 50 units from each factory to a distribution center, from which up to 50 units can be shipped to each warehouse. The shipping cost per unit for each alternative is shown in the following table, along with the amounts to be produced at the factories and the amounts needed at the warehouses. To From Factory 1 Factory 2 Distribution center Allocation Unit Shipping Cost Distribution Center 3 4 Warehouse 1 2 7 2 60 9 4 90 Output 80 70 (a) Formulate the network representation of this problem as a minimum cost flow problem. (b) Formulate the linear programming model for this problem.

A company will be producing the same new product at two different factories, and then the product must be shipped to two warehouses. Factory 1 can send an unlimited amount by rail to warehouse 1 only, whereas factory 2 can send an unlimited amount by rail to warehouse 2 only. However, independent truckers can be used to ship up to 50 units from each factory to a distribution center, from which up to 50 units can be shipped to each warehouse. The shipping cost per unit for each alternative is shown in the following table, along with the amounts to be produced at the factories and the amounts needed at the warehouses. To From Factory 1 Factory 2 Distribution center Allocation Unit Shipping Cost Distribution Center 3 4 Warehouse 1 2 7 2 60 9 4 90 Output 80 70 (a) Formulate the network representation of this problem as a minimum cost flow problem. (b) Formulate the linear programming model for this problem.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 73P
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A company will be producing the same new product at two different factories, and then the product must be shipped to two warehouses. Factory 1 can send an unlimited amount by rail to warehouse 1 only, whereas factory 2 can send an unlimited amount by rail to warehouse 2 only. However, independent truckers can be used to ship up to 50 units from each factory to a distribution center, from which up to 50 units can be shipped to each warehouse. The shipping cost per unit for each alternative is shown in the following table, along with the amounts to be produced at the factories and the amounts needed at the warehouses. From Factory 1 Factory 2 To Distribution center Allocation Unit Shipping Cost Distribution Center 3 4 Warehouse 1 7 2 60 2 9 4 90 Output 80 70 (a) Formulate the network representation of this problem as a minimum cost flow problem. (b) Formulate the linear programming model for this problem.
Transcribed Image Text:A company will be producing the same new product at two different factories, and then the product must be shipped to two warehouses. Factory 1 can send an unlimited amount by rail to warehouse 1 only, whereas factory 2 can send an unlimited amount by rail to warehouse 2 only. However, independent truckers can be used to ship up to 50 units from each factory to a distribution center, from which up to 50 units can be shipped to each warehouse. The shipping cost per unit for each alternative is shown in the following table, along with the amounts to be produced at the factories and the amounts needed at the warehouses. From Factory 1 Factory 2 To Distribution center Allocation Unit Shipping Cost Distribution Center 3 4 Warehouse 1 7 2 60 2 9 4 90 Output 80 70 (a) Formulate the network representation of this problem as a minimum cost flow problem. (b) Formulate the linear programming model for this problem.
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