4. (25 points) Ali Baba has 3 farms scattered around the country. They raise cattle on these farms and sell them to the country's four largest slaughterhouses. Every Monday, Ali Baba receives orders from slaughterhouses and makes a weekly transportation plan between farms and slaughterhouses to meet the demands. If the demand for a slaughterhouse cannot be met, they must pay a fine. See Table 1 for the fines specific for the slaughterhouses. This week, the demands of the slaughterhouses occurred as in Table 1. The weekly capacity of the farms is given in Table 2. Ali Baba has a contract with a transportation company for carrying the cattle. They pay 0.3 TL per cattle per kilometer for transportation. The distances between farms and slaughterhouses are given in Table 3. For instance, if they carry 10 cattle from Erzurum to stanbul, the cost will be 0.3*10*1350 = 4050 TL. Ali Baba wants to make this week's plan at the lowest cost. a) Formulate the problem as a transportation problem. Built the balanced transportation table. b) Find a basic feasible solution to the problem using minimum cost method. c) Evaluate whether the basic feasible solution found in part b is optimal or not. Table 1. Slaughterhouses Locations of Slaughterhouses istanbul Ankara zmir Adana Demand (cattle) Fine for unmet demand (TL per cattle) 380 550 250 600 200 450 170 500 Table 2. Farms Farms Erzurum Tekirda Denizli Capacity (cattle per week) 370 290 250 Table 3. Distance between farms and slaughterhouses (in km.) stanbul Ankara zmir Erzurum 1350 870 1470 Tekirda 150 390 Denizli 570 470 240 Adana 810 1070 730 590 4. (25 points) Ali Baba has 3 farms scattered around the country. They raise cattle on these farms and sell them to the country's four largest slaughterhouses. Every Monday, Ali Baba receives orders from slaughterhouses and makes a weekly transportation plan between farms and slaughterhouses to meet the demands. If the demand for a slaughterhouse cannot be met, they must pay a fine. See Table 1 for the fines specific for the slaughterhouses. This week, the demands of the slaughterhouses occurred as in Table 1. The weekly capacity of the farms is given in Table 2. Ali Baba has a contract with a transportation company for carrying the cattle. They pay 0.3 TL per cattle per kilometer for transportation. The distances between farms and slaughterhouses are given in Table 3. For instance, if they carry 10 cattle from Erzurum to stanbul, the cost will be 0.3*10*1350 = 4050 TL. Ali Baba wants to make this week's plan at the lowest cost. a) Formulate the problem as a transportation problem. Built the balanced transportation table. b) Find a basic feasible solution to the problem using minimum cost method. c) Evaluate whether the basic feasible solution found in part b is optimal or not. Table 1. Slaughterhouses Locations of Slaughterhouses istanbul Ankara zmir Adana Demand (cattle) Fine for unmet demand (TL per cattle) 380 550 250 600 200 450 170 500 Table 2. Farms Farms Erzurum Tekirda Denizli Capacity (cattle per week) 370 290 250 Table 3. Distance between farms and slaughterhouses (in km.) stanbul Ankara zmir Erzurum 1350 870 1470 Tekirda 150 390 Denizli 570 470 240 Adana 810 1070 730 590
