Consider a regional power system with three generating stations: A, B, and C. Each station serves its own local area. Three outlying areas are also served by the system: X, Y, and Z. The power demanded at areas X, Y, and Z is 25 MW (megawatts), 50 MW, and 30 MW, respectively. The maximum generating capacity beyond local requirements and the cost of generation at the three stations is shown in the table.
Power can be transmitted between any pair of generating stations, but 5% of the amount is lost. Power can be transmitted from some of the generating stations to the outlying areas, but 10% of the amount is lost. Lines exist from stations A and C to X, from B and C to Y, and from A and B to Z. Our goal is find the minimum cost power distribution plan between generating stations and to outlying areas.