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 each plant to each warehouse are as follows. Customer demand and shipping costs per unit (in \$) from each warehouse to each customer are as follows. (a) Develop a network representation of this problem. (Submit a file with a maximum size of 1 MB.) No file chosen (c) Solve the linear proqram to determine the optimal shipping plan. units shipped from node i to node j.) Min s.t. Plant 1 Production Plant 2 Production Plant 3 Production Warehouse 1 Shipments Warehouse 2 Shipments Customer 1 Orders Customer 2 Orders Customer 3 Orders Customer 4 Orders xij0foralli,j