Question 1. Developing an LP Model (60 points) Sealso 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 number of tons of coal demanded by each customer are given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contain at most 5% ash and at most 4% sulfur. Formulate an LP that minimizes the cost of meeting customer demands. Table 1 Production Cost ($) 50 Mine 1 2 3 Capacity 120 100 140 Ash Content (tons) 0.08 0.06 0.04 Sulfur Content (tons) 0.05 0.04 0.03 55 62 Table 2 Customer 1 80 Customer 2 70 Customer 3 60 Customer 4 40 Table 3 Mine (i) 1 2 6 Customer (i) 3 8 1 4 9 8 4 12 11 5 2 3 6 12 7 3 Hint: Decision variable: Xij: the amount of coal produced in mine i, which is transported to customer j. Question 1. Developing an LP Model (60 points) Sealso produces coal at three mines and ships it to four customers. The cost per ton of producing coal, the ash and sulfur content (per ton) of the coal, and the production capacity (in tons) for each mine are given in Table 1. The number of tons of coal demanded by each customer are given in Table 2. The cost (in dollars) of shipping a ton of coal from a mine to each customer is given in Table 3. It is required that the total amount of coal shipped contain at most 5% ash and at most 4% sulfur. Formulate an LP that minimizes the cost of meeting customer demands. Table 1 Production Cost ($) 50 Mine 1 2 3 Capacity 120 100 140 Ash Content (tons) 0.08 0.06 0.04 Sulfur Content (tons) 0.05 0.04 0.03 55 62 Table 2 Customer 1 80 Customer 2 70 Customer 3 60 Customer 4 40 Table 3 Mine (i) 1 2 6 Customer (i) 3 8 1 4 9 8 4 12 11 5 2 3 6 12 7 3 Hint: Decision variable: Xij: the amount of coal produced in mine i, which is transported to customer j