The texas Corporation has four oil fields,four refineries and four distribution centers in the locations identified in the next tables. A major strike involving the transportation industries now has sharply curtailed Texago's capacity to ship oil from the four oil fields to thefour refineries to the distribution centers.
Refinery
Oilfield
NO C S ST
Texas 11 7 2 8
Califo 5 4 8 7
Ala 7 3 12 6
Mid 8 9 4 15
Distribution Center
P A KA SF
New 5 9 6 4
Charle 8 7 9 5
Seattle 4 6 7 8
St. Lo 12 11 9 7
a. Draw a rough map that shows the location of Texas oil fields, refineries, and distribution centers. Add arrows to show the flow of crude oil and the petroleum products through distribution network.
b. Redraw this distribution network by lining up all the nodes representing oil fields in one column, all the nodes representing refineries in asecond column, and all the nodes representing distribution centers in a third column. Then add arcs to show the possible flow.
c. Use the distribution network from part b to formulate a network model for Texago's problem as a variant of a maximum flow problem.
d. Formulate and solve a spreadsheet model for this problem.