Blue Ridge Power and Light Company generates electrical power at four coal-fired power plants along the eastern

Question:

Blue Ridge Power and Light Company generates electrical power at four coal-fired power plants along the eastern seaboard in Virginia, North Carolina, Maryland, and Delaware. The company purchases coal from six producers in southwestern Virginia, West Virginia, and Kentucky. Blue Ridge has fixed contracts for coal delivery from the following three coal producers:

The power-producing capabilities of the coal produced by these suppliers differs according to the quality of the coal. For example, coal produced by ANCO provides 26.2 million BTUs per ton, while coal produced at Boone Creek provides 27.1 million BTUs per ton. Blue Ridge also purchases coal from three backup auxiliary suppliers, as needed (i.e., it does not have fixed contracts with these producers). In general, the coal from these backup suppliers is more costly and lower grade.

The demand for electricity at Blue Ridgeâ€™s four power plants is as follows (note that it requires approximately 10 million BTUs to generate 1 megawatt hour):
Electricity
Power Plant ......... Demand (million BTUs)
1. Afton ............ 4,600,000
2. Surrey ........... 6,100,000
3. Piedmont .......... 5,700,000
4. Chesapeake .......... 7,300,000
For example, the Afton plant must produce at least 4,600,000 million BTUs next year, which translates to approximately 460,000 megawatt hours.
Coal is primarily transported from the producers to the power plants by rail, and the cost of processing coal at each plant is different. Following are the combined transportation and processing costs for coal from each supplier to each plant.

Formulate and solve a linear programming model to determine how much coal should be purchased and shipped from each supplier to each power plant in order to minimizecost.