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Problem 2: (35 Points) Min-Cost-Flow by Network Simplex Method A company will be producing the same new product at two different factories, this product must be shipped to two warehouses. Factory 1 can send an unlimited amount by rail to Warehouse 1, whereas Factory 2 can send an unlimited amount by rail to Warehouse 2 only. Additionally, independent truckers may be used to ship up to 50 units from each factory to a Distribution Center. From the Distribution Center, 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 each factory and the amounts needed at each warehouse. a) (10 Points) Represent the above problem as a graphical network - Be sure to draw necessary nodes and define node values - Be sure to draw necessary arcs and describe arc costs and any capacities b) (25 Points) Solve the represented problem as a min-cost-flow problem using the Network Simplex method - Use the following starting solution: - Flow from Factory 1 to Warehouse 1: 60 Units - Flow from Factory 1 to Distribution Center. 20 Units - Flow from Factory 2 to Warehouse 2: 70 Units - Flow from Distribution Center to Warehouse 2: 20 Units - Make sure to show all completed calculations at each iteration - Show spanning tree and total cost of solution - Show determination of entering arc - Show determination of leaving arc