1. Connellsville Coal Company (30 points) Suppose that CCC Inc. (Connellsville Coal Company) sells three types of coal: Type A, Type B, and Type C. Type A coal comes directly from one of its mines and so does Type C. The weekly mining capacity for Type A coal is 1000 tons and for Type C it is 1500 tons. Type B, however, is not mined. Rather it is produced by simply blending Type A and Type C coal. Type A and Type C coal have the following characteristics: A Coal Dust (lbs/ton) Steam (lbs/ton) Mining Cost ($/ton) 3 24,000 $10 C 7 36,000 $15 The blended Type B coal is guaranteed to have no more than 4 lbs of coal dust per ton and no less than 25,000 lbs of steam produced per ton. The company can sell as much of Type A, B and C coal that it can produce. Excluding the cost of coal, based on current prices the contributions to profit for next week are $50 per ton for Type A, $40 per ton for Type B, and $35 per ton for Type C. The company has a commitment to sell at least 500 tons of Type B coal. Also, because of market constraints, it can sell no more than 1000 tons of Type A. Note: Simplify as much as possible. Have all variables on one side with no variables in the denominator. Hint: See Unit 4B Practice Problem #2 (a) State the decisions to be made, the objective and the constraints in words using = or = in the constraints. (Submit copy of Handwritten answer, 5 pts) (b) Define your decisions algebraically as decision variables. Then, using your objective and constraints in part (a), formulate the problem as an algebraic linear optimization model. (Submit copy of Handwritten answer, 5 pts) (c) Set each of your decisions in part (a) equal to 500 and then compute the corresponding numerical values for your objective and constraints. Is this solution feasible and what is the corresponding value of the objective? (Submit copy of Handwritten answer, 5 pts) (d) Write your algebraic model from part (c) as an EXCEL model. (Submit answer in an Excel file, 5 pts) (e) Using your EXCEL model with a value of 500 for each decision cell, compute the values for the objectives and the constraints. Do you get the same values as in part (b)? (Submit answer in an Excel file, 5 pts) (f) Optimize your EXCEL model using Solver and give the Answer and Sensitivity Reports. From the Answer Report, what is the optimal solution and the optimal value of the objective? (Submit model, Answer and Sensitivity Reports. Submit copy of your Handwritten optimal solution and optimal value of the objective, 5 pts)