Coalco produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The cost (n dollars) of shipping a ton of coal from a mine to each customer is given in Table 2. Also in Table 2 are the number of tons of coal demanded by each customer. It is required that the total amount of coal shipped contain at most 5% ash and at most 4% sulfur.
Table 1. Production Cost, Production Capacity, and Ash and Sulfur Content.
Production Ash Sulfur
Mine Cost ($) Capacity Content (tons) Content (Tons)
1 50 120 0.08 0.05
2 55 100 0.06 0.04
3 62 140 0.05 0.03
Table 2. Shipping Cost and Demand
Customer
Mine 1 2 3 4
1 4 6 8 12
2 9 6 7 11
3 8 12 3 5
Demand 80 70 60 40