5.8 (Use northwest-corner, least-cost, and Vogel methods for the starting initial solution, then use the one with least cost to find the optimal solution)

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. TABLE 5.26 Mileage Chart for Problem 5-8 Distribution area Refinery 1 Refinery 2 Refinery 3 \begin{tabular}{|ccc|} \multicolumn{1}{c}{1} & 2 & 3 \\ \hline 180 & 180 & - \\ 300 & 800 & 900 \\ 220 & 200 & 120 \\ \hline \end{tabular} 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. TABLE 5.26 Mileage Chart for Problem 5-8 Distribution area Refinery 1 Refinery 2 Refinery 3 \begin{tabular}{|ccc|} \multicolumn{1}{c}{1} & 2 & 3 \\ \hline 180 & 180 & - \\ 300 & 800 & 900 \\ 220 & 200 & 120 \\ \hline \end{tabular}