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Problem 4 (25 points): 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. Unit Shipping Cost To | Distribution Center | Warehouse 1 | Warehouse 2 | Output From | | | | Factory 1 | 3 | 7 | — | 80 Factory 2 | 4 | — | 9 | 70 Distribution center | | 2 | 4 | Allocation | | 60 | 90 | (a) Formulate the network representation of this problem as a minimum cost flow problem. (b) Formulate a linear programming model for this problem. (Bonus 10 Points) Use the network simplex algorithm to solve this problem and write down the minimum cost flow in the format of an optimal solution to part (b) .

          Problem 4 (25 points):

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.

Unit Shipping Cost
To | Distribution Center | Warehouse 1 | Warehouse 2 | Output
From | | | |
Factory 1 | 3 | 7 | — | 80
Factory 2 | 4 | — | 9 | 70
Distribution center | | 2 | 4 |
Allocation | | 60 | 90 |

(a) Formulate the network representation of this problem as a minimum cost flow problem.
(b) Formulate a linear programming model for this problem.

(Bonus 10 Points) Use the network simplex algorithm to solve this problem and write down the minimum cost flow in the format of an optimal solution to part (b) .

Problem 4 (25 points):

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.

Unit Shipping Cost
To | Distribution Center | Warehouse 1 | Warehouse 2 | Output
From | | | |
Factory 1 | 3 | 7 | — | 80
Factory 2 | 4 | — | 9 | 70
Distribution center | | 2 | 4 |
Allocation | | 60 | 90 |

(a) Formulate the network representation of this problem as a minimum cost flow problem.
(b) Formulate a linear programming model for this problem.

(Bonus 10 Points) Use the network simplex algorithm to solve this problem and write down the minimum cost flow in the format of an optimal solution to part (b) .

Added by Brandy R.

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