The Widget Company is fully integrated and produces goods and sells them at its retail outlets. After production at one of its two plants (P), the goods are stored in the company's three warehouses (W) until they are transported to the company's two retail outlets (RO). Trucks are used to transport the goods from the two plants to the warehouses, and then from the warehouses to the retail outlets. Using units of full truckloads, the first table below shows each plant's monthly output, its shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per month to each warehouse. For each retail outlet (RO), the second table below shows its monthly demand, its shipping cost per truckload from each warehouse, and the maximum amount that can be shipped per month from each warehouse. Management now wants to determine a distribution plan (number of truckloads shipped per month from each plant to each warehouse and from each warehouse to each retail outlet) that will minimize the total shipping cost. Table 1: Table 2: a) Draw a network that shows the company's distribution network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. b) Formulate a network model for this problem as a minimum-cost flow problem by inserting all the necessary data into the network drawn in part a). Make sure to include both the unit shipping cost as well as the shipping capacity information, as well as the supply and demand. c) Use Excel's Solver to find the optimal solution and describe it (i.e., what is the overall cost, how many units should be shipped from each plant to each warehouse and from each warehouse to each retail outlet), making sure that supply, demand, and capacity constraints are met. VOTE: Make sure that for each warehouse, the sum of inflows equals the sum of outflows (since hey are transshipment nodes)