Virginia Tech operates its own power generating plant The el

Virginia Tech operates its own power generating plant. The electricity generated by this plant supplies power to the university and to local businesses and residences in the Blacksburg area. The plant burns three types of coal, which produce steam that drives 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 result from burning a ton of each type of coal.

Amount Required Per

Coal

Sulfur

(in ppm)

Coal Dust

(in kg)

Pounds of Steam Produced

1

1,100

1.7

24,000

2

3,500

3.2

36,000

3

1,300

2.4

28,000

The three types of coal can be mixed and 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 emission (in ppm) resulting from burning one ton of this blend is:

The manager 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.

How would you formulate (set up) a linear programming model for this?

Solution

Ans:

Max 24,000C1 + 36,000C2 + 28,000C3       

St

C1+C2+C3 = 1                                               

1100C1+3500C2+1300C3 <= 2500              

1.7C1 +3.2C2 + 2.4C3 <= 2.8

C1, C2, C3 >= 0