Ajax produces detergent at five different plants. The capacity (in tons) of each plant is given in Table 1. The detergent is sent from the plants to the warehouses, where it is stored until it is shipped to the customers. The per-ton cost (in hundreds of dollars) of producing detergent at each plant and shipping it to each warehouse is given in Table 2. Ajax has four customers. The cost of shipping a ton of detergent from each warehouse to each customer is as given in Table 3. Each customer must be delivered the amount (in tons) o detergent given in Table 4. Table 1 Table 4 Plant Customer 1 2 3 4 2 3 Tons 300 200 300 200 400 Demand 200 300 150 250 Table 2 Table 5 From Warehouse 1 Warehouse 2 Warehouse 3 Facility Fixed Annual Cost (in Thousands) $ 10 5 Plant 1 Plant 2 Plant 3 Plant Plant 5 8 7 8 5 7 6 12 7 S 7 5 6 6 Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Warehouse 1 Warehouse 2 Warehouse 3 35 45 40 42 40 30 40 30 Table 3 From Customer 1 Customer 2 Customer 3 Customer 4 Warehouse 1 Warehouse 2 Warehouse 3 40 70 80 80 70 30 90 60 50 50 80 60 a) Formulate linear programming model whose solution will tell us how to minimize the cost of meeting the customer demands. Clearly identify the meaning of the decision variables. b) Modify the original problem if these are annual demands and there are a fixed annual cost of operating each plant and warehouse. The fixed annual costs (in thousands) are given in Table 5. Clearly identify the meaning of the decision variables. . c) Modify the model in part (b) by incorporating these additional constraints. Introduce additional variables as necessary. Each part below is independent of the other ones. If plant 3 is used, then warehouse 1 must also be used. At most 3 plants can be used. If plant 2 is used, then it must only ship to warehouse 1 or to warehouse 2 (exclusive OR). If warehouse 1 is used, then warehouse 2 must receive all their shipments from plant 2. Suppose customer demands in Table 4 are reduced by 50%. Now, model the condition that if plant 2 is used, then plants 3 and 4 can't be used. Ajax produces detergent at five different plants. The capacity (in tons) of each plant is given in Table 1. The detergent is sent from the plants to the warehouses, where it is stored until it is shipped to the customers. The per-ton cost (in hundreds of dollars) of producing detergent at each plant and shipping it to each warehouse is given in Table 2. Ajax has four customers. The cost of shipping a ton of detergent from each warehouse to each customer is as given in Table 3. Each customer must be delivered the amount (in tons) o detergent given in Table 4. Table 1 Table 4 Plant Customer 1 2 3 4 2 3 Tons 300 200 300 200 400 Demand 200 300 150 250 Table 2 Table 5 From Warehouse 1 Warehouse 2 Warehouse 3 Facility Fixed Annual Cost (in Thousands) $ 10 5 Plant 1 Plant 2 Plant 3 Plant Plant 5 8 7 8 5 7 6 12 7 S 7 5 6 6 Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Warehouse 1 Warehouse 2 Warehouse 3 35 45 40 42 40 30 40 30 Table 3 From Customer 1 Customer 2 Customer 3 Customer 4 Warehouse 1 Warehouse 2 Warehouse 3 40 70 80 80 70 30 90 60 50 50 80 60 a) Formulate linear programming model whose solution will tell us how to minimize the cost of meeting the customer demands. Clearly identify the meaning of the decision variables. b) Modify the original problem if these are annual demands and there are a fixed annual cost of operating each plant and warehouse. The fixed annual costs (in thousands) are given in Table 5. Clearly identify the meaning of the decision variables. . c) Modify the model in part (b) by incorporating these additional constraints. Introduce additional variables as necessary. Each part below is independent of the other ones. If plant 3 is used, then warehouse 1 must also be used. At most 3 plants can be used. If plant 2 is used, then it must only ship to warehouse 1 or to warehouse 2 (exclusive OR). If warehouse 1 is used, then warehouse 2 must receive all their shipments from plant 2. Suppose customer demands in Table 4 are reduced by 50%. Now, model the condition that if plant 2 is used, then plants 3 and 4 can't be used
