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Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residents in the Blacksburg area. The plant burns three types of coal, which produce steam that rives the turbines that generate the electricity. The Environmental Protection Agency (EPA) requires that for each ton of coal burned, the emissions from the coal furnace smoke stacks contain no more than 2,500 parts per million (ppm) of sulfur and no more than 2.8 kilograms (kg) of coal dust. The following table summarizes the amounts of sulfur, coal dust, and steam that results from burning a ton of each type of coal. Sulfur (in Coal Dust (in kg) Pounds of Steam Coal ppm) Produced 1 1,100 1.7 24,000 3,500 3.2 36,000 1,300 2.4 28,000 Max Allowed 2,500 2.8 The three types of coal can be mixed an burned in any combination. The resulting emission of sulfur or coal dust and the pounds of steam produced by any mixture are given as the weighted average of the values shown in the table for each type of coal. For Example, if the coals are mixed to produce a blend that consists of 35% of coal 1, 40% of coal 2, and 25% of coal 3, the sulfur emissions (in ppm) resulting from burning one ton of this blend is: 0.35 x 1,100 + 0.40 x 3,500 + 0.25 x 1,300 = 2,110 The manage of this facility wants to determine the blend of coal that will produce the maximum pounds of steam per ton without violating the EPA requirements.

Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residents in the Blacksburg area. The plant burns three types of coal, which produce steam that rives the turbines that generate the electricity. The Environmental Protection Agency (EPA) requires that for each ton of coal burned, the emissions from the coal furnace smoke stacks contain no more than 2,500 parts per million (ppm) of sulfur and no more than 2.8 kilograms (kg) of coal dust. The following table summarizes the amounts of sulfur, coal dust, and steam that results from burning a ton of each type of coal. Sulfur (in Coal Dust (in kg) Pounds of Steam Coal ppm) Produced 1 1,100 1.7 24,000 3,500 3.2 36,000 1,300 2.4 28,000 Max Allowed 2,500 2.8 The three types of coal can be mixed an burned in any combination. The resulting emission of sulfur or coal dust and the pounds of steam produced by any mixture are given as the weighted average of the values shown in the table for each type of coal. For Example, if the coals are mixed to produce a blend that consists of 35% of coal 1, 40% of coal 2, and 25% of coal 3, the sulfur emissions (in ppm) resulting from burning one ton of this blend is: 0.35 x 1,100 + 0.40 x 3,500 + 0.25 x 1,300 = 2,110 The manage of this facility wants to determine the blend of coal that will produce the maximum pounds of steam per ton without violating the EPA requirements.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
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Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residents in the Blacksburg area. The plant burns three types of coal, which produce steam that rives the turbines that generate the electricity. The Environmental Protection Agency (EPA) requires that for each ton of coal burned, the emissions from the coal furnace smoke stacks contain no more than 2,500 parts per million (ppm) of sulfur and no more than 2.8 kilograms (kg) of coal dust. The following table summarizes the amounts of sulfur, coal dust, and steam that results from burning a ton of each type of coal. Sulfur (in Coal Dust Pounds of Steam Coal ppm) (in kg) Produced 1 1,100 1.7 24,000 3,500 3.2 36,000 1,300 2.4 28,000 Max Allowed 2,500 2.8 The three types of coal can be mixed an burned in any combination. The resulting emission of sulfur or coal dust and the pounds of steam produced by any mixture are given as the weighted average of the values shown in the table for each type of coal. For Example, if the coals are mixed to produce a blend that consists of 35% of coal 1, 40% of coal 2, and 25% of coal 3, the sulfur emissions (in ppm) resulting from burning one ton of this blend is: 0.35 x 1,100 + 0.40 x 3,500 + 0.25 x 1,300 = 2,110 The manage of this facility wants to determine the blend of coal that will produce the maximum pounds of steam per ton without violating the EPA requirements.
Transcribed Image Text:Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residents in the Blacksburg area. The plant burns three types of coal, which produce steam that rives the turbines that generate the electricity. The Environmental Protection Agency (EPA) requires that for each ton of coal burned, the emissions from the coal furnace smoke stacks contain no more than 2,500 parts per million (ppm) of sulfur and no more than 2.8 kilograms (kg) of coal dust. The following table summarizes the amounts of sulfur, coal dust, and steam that results from burning a ton of each type of coal. Sulfur (in Coal Dust Pounds of Steam Coal ppm) (in kg) Produced 1 1,100 1.7 24,000 3,500 3.2 36,000 1,300 2.4 28,000 Max Allowed 2,500 2.8 The three types of coal can be mixed an burned in any combination. The resulting emission of sulfur or coal dust and the pounds of steam produced by any mixture are given as the weighted average of the values shown in the table for each type of coal. For Example, if the coals are mixed to produce a blend that consists of 35% of coal 1, 40% of coal 2, and 25% of coal 3, the sulfur emissions (in ppm) resulting from burning one ton of this blend is: 0.35 x 1,100 + 0.40 x 3,500 + 0.25 x 1,300 = 2,110 The manage of this facility wants to determine the blend of coal that will produce the maximum pounds of steam per ton without violating the EPA requirements.
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