3. A Makonsel company is a fully integrated company that both produces goods and sells them at its retail outlets. After production, the goods are stored in the company’s two warehouse until needed by the retail outlet. Trucks are used to transport the goods from the two plants to the warehouses, and then from the warehouses to the three retail outlets. Using units of full truckloads, the following table shows each plants monthly output, its shipping cost per truckload send to each warehouse, and the maximum amount that it can ship per month to each warehouse. From/To Unit shipping cost Shipping capacity Output W1 W2 W1 W2 Plant 1 $450 $560 125 150 225 Plant 2 510 600 175 200 300 For each retail outlet (RO), the next table shows its monthly demand, its shipping costs per truckload from each warehouse, and the maximum amount that can be shipped per month from each warehouse. From/To Unit shipping cost Shipping capacity R01 RO2 RO3 R01 RO2 RO3 W1 $470 $505 $495 100 150 100 W2 390 415 440 125 150 75 Demand 175 200 150 175 200 150 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. (a) Draw a network that depicts the company’s distribution network. Be sure to clearly and neatly label all nodes. (b) Formulate this problem as a network (minimum cost flow) problem. (c) Solve the model using Python and Gurobi.
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