Please use the transportation model and the northwest-corner method or the least-cost method.

Problem 5-5. In Example 5.1-2, suppose that for the case where the demand exceeds the supply (Table 5.4), a penalty is levied at the rate of $200 and $300 for each undelivered car at Denver and Miami, respectively. Additionally, no deliveries are made from the Los Angeles plant to the Miami distribution center. Set up the model, and determine the optimal shipping schedule for the problem. Example 5.1-2 In the MG model, suppose that the Detroit plant capacity is 1300 cars (instead of 1500). The total supply (= 3500 cars) is less than the total demand = 3700 cars), meaning that part of the demand at Denver and Miami will not be satisfied. Because the demand exceeds the supply, a dummy plant (source) with a capacity of 200 cars (=3700 3500 is added to balance the model. The unit transportation cost from the dummy plant to the two destinations is zero because the plant does not exist. Table 5.40 gives the balanced model together with its optimum solution. The solution shows that the dummy plant ships 200 cars to Miami, which means that Miami will be 200 cars short of satisfying its demand of 1400 cars. Table 5.4 MG Model with Dummy Plant Miami Supply Denver 80 215 Los Angeles 1000 1000 100 108 Detroit 1300 1300 102 68 New Orleans 1200 1200 Dummy Plant 200 1400 Demand 2300 Problem 5-5. In Example 5.1-2, suppose that for the case where the demand exceeds the supply (Table 5.4), a penalty is levied at the rate of $200 and $300 for each undelivered car at Denver and Miami, respectively. Additionally, no deliveries are made from the Los Angeles plant to the Miami distribution center. Set up the model, and determine the optimal shipping schedule for the problem. Example 5.1-2 In the MG model, suppose that the Detroit plant capacity is 1300 cars (instead of 1500). The total supply (= 3500 cars) is less than the total demand = 3700 cars), meaning that part of the demand at Denver and Miami will not be satisfied. Because the demand exceeds the supply, a dummy plant (source) with a capacity of 200 cars (=3700 3500 is added to balance the model. The unit transportation cost from the dummy plant to the two destinations is zero because the plant does not exist. Table 5.40 gives the balanced model together with its optimum solution. The solution shows that the dummy plant ships 200 cars to Miami, which means that Miami will be 200 cars short of satisfying its demand of 1400 cars. Table 5.4 MG Model with Dummy Plant Miami Supply Denver 80 215 Los Angeles 1000 1000 100 108 Detroit 1300 1300 102 68 New Orleans 1200 1200 Dummy Plant 200 1400 Demand 2300