4. A company manufactures three different chemical products from feedstock using five possible processes A, B, C, D, and

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4 A Company Manufactures Three Different Chemical Products From Feedstock Using Five Possible Processes A B C D And 1 (99.94 KiB) Viewed 53 times

4. A company manufactures three different chemical products from feedstock using five possible processes A, B, C, D, and R. The following diagram summarises the connections of the production facility: Feedstock Intermediate Waste O B The yields and costs of the processes are as follows: Process A B с D R Feed Inter Waste 0 02 03 (tonnes) (tonnes) (tonnes) (tonnes) (tonnes) (tonnes) -1 0.5 0.4 0.1 -1 0.55 0.37 0.08 -1 0.4 0.2 0.4 - 1 0.3 0.3 0.4 0.3 - 1 Cost Limit (£/t) (t/hr) 32 50 31 50 25 50 35 50 45 60 For example, process C produces 0.4 t of waste, 0.2 t of O, and 0.4 t of O2 from a tonne of the intermediate product, at a cost of £25 per tonne of input, and can process at most 50 t of the intermediate product per hour. Feedstock costs £2.80 per tonne. Waste product (untreated process R) cannot be disposed of by the plant. The selling prices of 0, 0, and Og are £210.00 per tonne, £175.00 per tonne and £190.00 per tonne respectively. We assume that no limit exists on the quantity of any product that can be sold. Find the production plan which maximises the profit. You should follow the following steps: (a) Generate a LP formulation for the problem. This should include: the decision variables, including their precise description and units, the objective and the constraints. (b) Solve it using Xpress/IVE. Provide a file containing your codes with annotations, so each line of code is explained. (Hint for writing the program: you should use array's, sum's and forall's for the cost in the objective and for the limit constraints). (c) Present an interpretation of the solution. The interpretation of the solution should have the form of a production plan that a production manager would easily understand: it should give the amount of feedstock bought per hour, the amount of input for each of the pro- cesses, as well as the amounts of products 01, 02, 03 made per hour and the total profit per hour. Marks [7]: 4(a), 2(b), 1(c)