Valley Electric Company generates electrical power at four coal-fired power plants in Nova Scotia, New Brunswick, Quebec, and Ontario. The company purchases coal from six producers in British Columbia, Alberta, and Saskatchewan. Valley Electric 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 APCO provides 27.2 million BTUs per tonne while coal produced at Balfour provides 28.1 million BTUs per tonne. Valley Electric also purchases coal from three back-up auxiliary suppliers as needed (i.e., it does not have fixed contracts wit these producers). In general, the coal from these back-up suppliers is more costly and lower grade:

The demand for electricity at Valley Electric€™s four power plants is as follows. (Note that it requires approximately 10 million BTUs to generate 1 MW hr):

For example, the Nova Scotia plant must produce at least 4,700,000 million BTUs next year, which translates to approximately 470,000 megawatt hours.

Coal is primarily transported from the producers to the power plants by rail and the cost of processing coal at each is different. Following are the combined transportation and processing costs for coal each 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 to minimize cost.

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Million Cost ($/tonne) BTUS/tonne 27.2 Coal Producer Tonnes APCO 24 APCO Balfour 180,000 315,000 27 28.1 Cannon 26.6 26 340,800 Available Cost Million ($/tonne) Coal Producer Denton BTUS/tonne Tonnes 33 22.4 115,000 ESCO 105,000 28 19.7 Frampton 36 24.6 185,000