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 produces 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 smokestacks contain no more than 2,500 parts per million (ppm) of sulfur and no more than 2.8 kilograms (kg) of coal dust. However, the managers of the plant are concerned about the environment and want to keep these emissions to a minimum. The following table summarizes the amounts of sulfur, coal dust, and steam that result from burning a ton of each type of coal.

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:
0.35 × 1,100 + 0.40 × 3,500 + 0.25 × 1,300 = 2,110
The manager of this facility wants to select a blend of coal to burn while considering the following objectives:
Objective 1: Maximize the pounds of steam produced.
Objective 2: Minimize sulfur emissions.
Objective 3: Minimize coal dust emissions.
a. Formulate an MOLP model for this problem and implement your model in a spreadsheet.
b. Determine the best possible value for each objective in the problem.
c. Determine the solution that minimizes the maximum percentage deviation from the optimal objective function values. What solution do you obtain?
d. Suppose management considers maximizing the amount of steam produced five times as important as achieving the best possible values for the other objectives. What solution does thissuggest?

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Sulfur (in ppm)(in Coal Dust Pounds of Steam Produced 24,000 36,000 28,000 Coal in ppmin kg) 1,100 3,500 1,300 1.7 3.2 2.4