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11. The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from cach plant to cach warehouse are as follows: Capacity Plant 1 2 3 Warehouse 1 2 4 7 8 5 5 6 450 600 380 Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows: 4 Warehouse 1 2 Demand 1 6 3 300 Customer 2 4 6 300 3 8 7 4 7 400 300 a. Develop a network representation of this problem. b. Formulate a linear programming model of the problem. c. Solve the linear program to determine the optimal shipping plan