Please answer 5-9 without using any computer programs or even excel.

5-8. 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 transported to the three distribution areas through a network of pipelines. The transportation cost is 10 cents per 1000 gallons per pipeline mile. Table 5.26 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. *5-9. In Problem 5-8, suppose that the capacity of refinery 3 is 6 million gallons only and that distribution area 1 must receive all its demand. Additionally, any shortages at areas 2 and 3 will incur a penalty of 5 cents per gallon. (a) Formulate the problem as a transportation model. (b) Determine the optimum shipping schedule. 5-10. In Problem 5-8, suppose that the daily demand at area 3 drops to 4 million gallons. Surplus production at refineries 1 and 2 is diverted to other distribution areas by truck. The transportation cost per 100 gallons is $1.50 from refinery 1 and $2.20 from refinery 2. Refinery 3 can divert its surplus production to other chemical processes within the plant. (a) Formulate the problem as a transportation model. (b) Determine the optimum shipping schedule. TABLE 5.26 Mileage Chart for Problem 5-8 Distribution area 2 3 Refinery 1 Refinery2 Refinery 3 120 300 200 180 100 250 80 120