Distributing Oil: Texxon Oil Distributors, Inc., has three active oil wells in a west Texas oil field. Well 1 has a capacity of 93 thousand barrels per day (TBD), Well 2 can produce 88 TBD, and Well 3 can produce 95 TBD. The company has five refineries along the Gulf Coast, all of which have been operating at stable demand levels. In addition, three pump stations have been built to move the oil along the pipelines from the wells to the refineries. Oil can flow from any one of the wells to any of the pump stations and from any one of the pump stations to any of the refineries, and Texxon is looking for a minimum-cost schedule. The refineries requirements are as follows.

Refinery	R1	R2	R3	R4	R5
Requirement (TBD)	30	57	48	91	48

The companys cost accounting system recognizes charges by the segment of pipeline that is used. These daily costs are given in the tables below, in dollars per thousand barrels.

To		Pump A	Pump B	Pump C
From	Well 1	1.52	1.6	1.4
	Well 2	1.7	1.63	1.55
	Well 3	1.45	1.57	1.3

To		R1	R2	R3	R4	R5
From	Pump A	5.15	5.69	6.13	5.63	5.8
	Pump B	5.12	5.47	6.05	6.12	5.71
	Pump C	5.32	6.16	6.25	6.17	5.87

1. Build a linear programming model for this distribution network design problem.

2. Use the Excel solver to solve the linear programming model

3. Show the network diagram corresponding to the solution. That is, label each of the arcs in the solution and verify that the flows are consistent with the given information.

4. If each pump station has a capacity, and the three pump stations maximum flow through them are all 100 TBD per day. What is optimal distribution plan (Hint: add a constraint to the mode1 in Q1 and then use excel solver to solve it)?