The Tri-State Oil Company refines its oil product at 2 sites (s1 and s2) and delivers the product

over leased pipelines to its final distribution depot, site s10. By contractual agreement, Tri-State

uses three pipeline companies, Anderson Co., Birdsong Biopipe and Carson Carriers, Inc. to

deliver its product.

Anderson charges Tri-State $100/unit/pipeline link for transporting the oil product, while

Birdsong charges $80/unit/pipeline link and Carson $60/unit/pipeline link. The oil product can

be shipped along any parts of the pipeline distribution network described in the spreadsheet, with

the final destination the depot s10. The table in the spreadsheet notes the 'to' and 'from' nodes,

the pipeline capacity and the company that owns the link. Site s1 can produce 10 units daily,

whereas site s2 can produce 12 units daily. There are some links with bi-directional flow

capabilities.

Besides the capacity constraints, there are two additional cost requirements that an optimal

distribution plan must have:

1) At most, $7000 (in total) can be spent in fees to the pipeline companies.

2) At least $1,500 must be spent with each pipeline company.

Develop an LP model that determines how many units to ship through the pipeline network,

maximizing the oil arriving at the depot s10 AND subject to the cost and pipeline restrictions

mentioned above.

From To Capacity Company From To Capacity Company $1 $3 10 Anderson $2 $4 12 Birdsong $3 $5 6 Anderson $3 $6 7 Carson $3 $4 8 Carson $4 $3 5 Carson $4 $7 5 Birdsong $5 $6 3 Carson $5 $8 7 Anderson $6 $5 3 Carson $6 $8 5 Carson $6 $7 4 Carson $7 4 Carson $7 $9 8 Birdsong s8 $9 6 Carson $10 11 Anderson $9 $8 6 Carson $9 $10 9 Birdsong