Question: A company will be producing the same new product at two different factories, and then shipping the product to two warehouses. 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. Unlimited amounts of the product can be shipped by rail from factory 1 to warehouse 1 , and from factory 2 to warehouse 2. However, rail cannot be used to ship units from factory 1 to warehouse 2, or from factory 2 to warehouse 1. The shipping cost per unit for each alternative is shown in the table below. Each factory has a capacity to produce 70 units per month and there is a monthly demand for 60 units at each warehouse.

Formulate a minimum cost network flow model to determine a production and distribution plan that meets the monthly demand at minimal cost.

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