The Willow Run Coal Company operates three mines in Kentucky and West Virginia and supplies coal to four utility power plants along the East Coast. The cost of shipping coal from each mine to each plant, the capacity at each of the four mines, and demand at each plant are shown in the following table:

The cost of mining and processing coal is $62 per ton at mine 1, $67 per ton at mine 2, and $75 per ton at mine 3. The percentage of ash and sulfur content per ton of coal at each mine is as follows:

Each plant has different cleaning equipment. Plant 1 requires that the coal it receives can have no more than 6% ash and 5% sulfur; plant 2 coal can have no more than 5% ash and sulfur combined; plant 3 can have no more than 5% ash and 7% sulfur; and plant 4 can have no more than 6% ash and sulfur combined. The company wants to determine the amount of coal to produce at each mine and ship to its customers that will minimize its total cost. Formulate and solve a linear programming model for thisproblem.

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Plant Mine 1 23 Mine Capacity tons) $7 9 10 12 9 7 8 12 11 5 7 220 190 280 Demand (tons0160 90 180 Mine 96 Ash % Sulfur