4. The ABC Corporation has one oil field, four refineries, three distribution centers, and one customer (oil company). Using units of thousands of barrels of crude oil (and its equivalent in refined products), the following tables show the maximum number of units that can be shipped per day from one oil field to each refinery, and from each refinery to each distribution center, and from each distribution center to one oil company. Oil Field Refinery R2 R3 7 2 R1 11 R4 0 8 Customer (Oil Company) Distribution Center D1 D2 D3 5 9 Refinery R1 R2 Distribution Center D1 D2 D3 8 7 8 7 R3 12 12 10 R4 9 4 The ABC management now wants to determine a plan for how many units to ship from one oil field to each refinery, from each refinery to each distribution center, and from each distribution center to one oil company that will maximize the total number of units reaching the one oil company. (a) Draw a distribution network by lining up a node representing one oil field in one column, all the nodes representing refineries in a second column, all the nodes representing distribution centers in a third column, and a node representing one oil company in one column. Then add arcs with their capacities to show the possible flow. (10 Points) (b) Formulate the maximum flow problem as a linear programming problem. (10 Points) (c) According to the optimal solution given below determine the objective value and the slack of each arc and fill the table below. (10 Points) Slack Value 26 9 7 2 8 5 4 Objective value: Variable XOR1 XOR2 XOR3 XOR4 XR1D1 XR1D2 XR2D1 XR2D2 XR3D1 XR3D3 XR4D2 XR4D3 XD1C XD2C XD3C 3 4 0 2 4 4 8 12 6 HAVE A GOOD LUCK