ProChem Inc. runs a complex chemical plant that runs 24-7. One section of the plant deals with the processing of two raw materials, I and II into four sellable products and waste. Process A combines the raw materials in a 2:3 ratio to produce Product 1, Product 3, and waste in a 3:5:2 ratio. This process takes 9 worker-hours of labor per ton of raw material processed. The machinery required for Process A can handle 0.75 tons of raw material per hour and costs $50 per hour to run. Process B is run in batches requiring exactly 1.5 tons of Raw Material I, 0.8 tons of Raw Material II, 3 hours on the appropriate machinery, and 14.5 worker-hours of labor. Process B produces 0.5 tons of Product 2 and 1.4 tons of Product 3, leaving 0.4 tons of waste. Process Bs machinery costs $25 per hour to run. Process C produces only Product 4. It consumes 0.6 tons of Product 1 and 1.2 tons of Product 2 for each ton of Product 4, generating 0.8 tons of waste in the process. Process D turns Product 3 and waste into Products 2 and 4. Equal amounts of each input are required. The process produces 1.5 tons of Product 4 for each ton of Product 2. Processes C and D run on the same machinery which can process 0.5 tons of input material per hour, costs $38 per hour to run, and requires 8 workers to constantly monitor it. Additionally, if Process C and D are both produced, the machinery needs to be shut down to be converted from one process to the other. The conversion process requires 15 hours (of clock time) and 20 worker-hours.

Our existing contracts with our suppliers requires them to deliver 90 tons of each raw material each week for a fixed charge. Another contractor disposes of remaining waste at a cost of $120 per ton. They can dispose of up to 5 tons of waste per week. Our contracts with our customers oblige us to deliver 25 tons of Product 1 and 30 tons of Product 2 per week at prices of $270 per ton and $310 per ton respectively. We could also sell up to 20 tons more of Product 2 per week at the same prices if it were available. Our contract for Product 3 is to deliver 75 tons per week at a price of $120 per ton. There is a mechanism in this contract for us to deliver less, but that incurs a penalty of $30 per ton we are short each week. Product 4 is sold on the retail market for $360 per ton. The corporate office is confident that this market could easily produce sales of up to 40 tons per week. Our current contract with the labor union pays workers $45 per hour. Formulate a linear program that maximizes the weekly profit of this division. You should submit: (a) A GNU MathProg file named username-exam1.2.mod containing: Note: One week contains 168 hours. In each process, the total weight of material going in is the same as the total weight of material going out. You do not need to account for labor scheduling. That will be determined at a separate time. Your solution will be implemented on an ongoing (cyclical) basis. As a result, you do not need to wait to start Processes C & D. The ingredients are already available from last week. Dont forget that, if you run both Process C and Process D, you have to shut down the machinery twice. Once to switch from C to D and once to switch back to C for the start of the next week. Optimal Objective Value: $136,754.29