The Big U operates a coal-fired power plant that burns 4,300 tons of coal per ye
ID: 406151 • Letter: T
Question
The Big U operates a coal-fired power plant that burns 4,300 tons of coal per year. Coals from four regions of the country can be burned in the plant. The amount of pollution produced depends on the amount of each type of coal burned. The details are in the table below, where the pounds of the various pollutants that are in each ton of coal that is burned are specified for each type of coal.
By federal law, the plant can emit at most 9,000, 6,000, and 2,500 pounds per year of fly ash, sulfur, and nitrogen oxide, respectively. Also, the state legislature requires that at least half of the coal burned come from Illinois.
1. Formulate a mathematical linear programming model for this problem.
2. Formulate your excel model and solve it with Solver in similar format.
3. Hint: this problem is a simpler version of Captain Wise example. Here the decision is only one dimensional: how many tons of coal to buy from each state.
Coal source (pounds of pollution/ton of coal burned) Fly ash Sulfur Nitrogen oxide Cost (S/ton) llinois 2.6 1.2 0.8 37 Kentucky 1.3 0.9 0.3 Pennsylvania 1.7 0.8 0.6 31 Wyoming 0.9 0.7 0.4Explanation / Answer
Mathematical linear programming model:
Assume the a.b.c. and d as the tons of coal bought from Illinois, Kentucky, Pensylvenia and Wyoming rspectively.
The constraints will be;
a+b+c+d = 4300
a>=2150 (as atlest half the quantity should be from Illinois)
2.6a + 1.3b + 1.7c + 0.9d <=9000
1.2a + 0.9 b + 0.8 c+ 0.7d<=6000
0.8a+0.3b+0.6c+0.4d<=2500
We have to Minimize the total cost,
Hence
Min. (37a+33b+31c+44d)
Illinois Ketucky Pennsylvania Wyoming fly ash 2.6 1.3 1.7 0.9 sulfur 1.2 0.9 0.8 0.7 NO 0.8 0.3 0.6 0.4 Cost ($/ton) 37 33 31 44 Illinois Ketucky Pennsylvania Wyoming quantity total cost 0Related Questions
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