2. In each of the following cases, determine whether a dummy source or a dummy destina tion must be added to balance the model. ‘ • (a) Supply: = 10, n, = 5. ^3 = 4, „^ = 5 Demand: 6, = 10, 6, = 5, ^3 = 7. 64 = 9 (b) Supply: a, = 30, a, = 44 Demand: A, = 25, bj = 30. 63 = 10 8. Three refineries with daily capacities of 6,5, and 8 million gallons, respectively, supply three distribution areas with daily demands of 4,8, and 7 million gallons, respectively Gasoline is TABLE 5.6 Price/Million kWh for Problem 6 City 1 2 3 1 $600 $700 $400 Plant 2 $320 $300 $350 3 $500 $480 $450 TABLE 5.7 Mileage Chart for Problem 8 Distribution area 1 2 3 1 120 180 Refinery 2 300 100 80 3 200 250 120 transported to the three distribution areas through a network of pipelines. The transportation cost is 10 cents per 1000 gallons per pipeline mile. Table 5.7 gives the mileage between the refineries and the distribution areas. Refinery 1 is not connected to distribution area 3. (a) Construct the associated transportation model. (b) Determine the optimum shipping schedule in the network. 12. Cars are shipped from three distribution centers to five dealers. The shipping cost is based on the mileage between the sources and the destinations and is independent of whether the truck makes the trip with partial or full loads. Table 5.9 summarizes the mileage between the distribution centers and ihe dealers together with the monthly TABLE 5.8 Transportation Cost/Crate for Problem 11 Retailer 1 2 3 4 1 $1 $2 $3 $2 Orchard 2 $2 $4 $1 $2 3 $1 $3 $5 $3 TABLE 5.9 Mileage Chart and Supply and Demand for Problem 12 Dealer 1 2 3 4 5 Supply 1 100 150 200 140 35 400 Center 2 50 70 60 65 80 200 3 40 90 100 150 130 150 Demand 100 200 150 160 140 supply and demand figures given in number of cars. A full truckload includes 18 cars. The transportation cost per truck mile is S25. (a) Formulate the associated transponation model. (b) Determine the optimal shipping schedule. _