Q2: Minimum cost flow problem 0 11 17 -2000 0 12 2000 0 -1000 13 3000 2 19 -4000 14 2000 20 -1500 16 3000 21 -1500 0 16 The 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 four warehouses until needed by the retail outlets. When the retailers need the products, the shipments might be shipped through 12 transshipment nodes where some clearance procedures are required before the shipments reach the retailers. Trucks are used to transport the goods from the four warehouses to the five retail outlets. The arc capacity is 1000 trucks for each arc. The number of trucks that can be shipped from each warehouse and the required number of trucks by the retailers is given in the figure. The costs of shipping are given in the table below. a) Formulate the problem as a minimum cost flow problem. b) Using the python, find the optimal distribution plan at minimum possible cost. c) Suppose that the demand of retailer 21 increases to 2000 products. How is it going to affect the formula, and what is the optimal distribution value? Use python to solve the problem. Attach the results as a picture. Also, in class, make the code ready so you can run it in front of your classmates. 2 From To Cost To Cost 1 5 9 From 12 12 6 1 6 6 6 6 1 2 7 7 5 6 6 7 9 9 7 6 6 10 12 12 13 13 13 17 18 19 14 17 18 2 5 5 7 5 8 2 2 8 6 13 3 7 13 19 8 10 8 15 3 3 3 5 5 10 9 9 4 7 7 6 14 14 14 14 14 7 7 7 4 8 4 9 9 7 7 5 5 10 4 10 14 5 5 17 18 19 20 21 19 20 21 15 21 6 15 6 5 5 5 6 5 8 15 15 11 12 12 13 14 10 7 7 7 10 8 16 16 6 7 10 6 6 6 7 7 7 7 11 12 13 10 7 8 7 8 6 8 8 7 9 14 8 9 8 6 8 15 16 13 9 9 9 9 14 15 9 10 9 7 8 5 10 7 5 10 10 15 10 16 11 12 11 17 10 Q2: Minimum cost flow problem 0 11 17 -2000 0 12 2000 0 -1000 13 3000 2 19 -4000 14 2000 20 -1500 16 3000 21 -1500 0 16 The 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 four warehouses until needed by the retail outlets. When the retailers need the products, the shipments might be shipped through 12 transshipment nodes where some clearance procedures are required before the shipments reach the retailers. Trucks are used to transport the goods from the four warehouses to the five retail outlets. The arc capacity is 1000 trucks for each arc. The number of trucks that can be shipped from each warehouse and the required number of trucks by the retailers is given in the figure. The costs of shipping are given in the table below. a) Formulate the problem as a minimum cost flow problem. b) Using the python, find the optimal distribution plan at minimum possible cost. c) Suppose that the demand of retailer 21 increases to 2000 products. How is it going to affect the formula, and what is the optimal distribution value? Use python to solve the problem. Attach the results as a picture. Also, in class, make the code ready so you can run it in front of your classmates. 2 From To Cost To Cost 1 5 9 From 12 12 6 1 6 6 6 6 1 2 7 7 5 6 6 7 9 9 7 6 6 10 12 12 13 13 13 17 18 19 14 17 18 2 5 5 7 5 8 2 2 8 6 13 3 7 13 19 8 10 8 15 3 3 3 5 5 10 9 9 4 7 7 6 14 14 14 14 14 7 7 7 4 8 4 9 9 7 7 5 5 10 4 10 14 5 5 17 18 19 20 21 19 20 21 15 21 6 15 6 5 5 5 6 5 8 15 15 11 12 12 13 14 10 7 7 7 10 8 16 16 6 7 10 6 6 6 7 7 7 7 11 12 13 10 7 8 7 8 6 8 8 7 9 14 8 9 8 6 8 15 16 13 9 9 9 9 14 15 9 10 9 7 8 5 10 7 5 10 10 15 10 16 11 12 11 17 10