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# Factory a factory b each unit of the standard

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factory A factory B grinding 80 60 polishing 60 75 Each unit of the standard and deluxe versions require 4 kg of raw material. The company has 120 kg of raw material available per week to allocate to the two factories. We would like to determine the number of standard and deluxe units to produce at each plant so that profit is maximized. First, let’s consider each factory in isolation. Assume for now that the company has decided to allocate 75 kg of raw material to factory A, and 45 kg of raw material to factory B per week. Let x 1 and x 2 represent the numbers of standard and deluxe units, respectively, to produce at factory A. The linear programming model to optimize profit at factory A is maximize 10 x 1 + 15 x 2 subject to 4 x 1 + 4 x 2 75 (raw material) 4 x 1 + 2 x 2 80 (grinding) 2 x 1 + 5 x 2 60 (polishing) x 1 ,x 2 0

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Similarly let x 3 and x 4 represent the numbers of standard and deluxe units to produce at factory B. The model for factory B is maximize 10 x 3 + 15 x 4 subject to 4 x 3 + 4 x 4 45 5 x 3 + 3 x 4 60 5 x 3 + 6 x 4 75 x 3 ,x 4 0 Translate the optimization problem for a single factory into AMPL. Note that there is really only one model, but there are two problem instances. You should create a single AMPL model ( factory.mod ) and two data files ( factoryA.dat and factoryB.dat ). This allows a clean separation of the model and data. You may then instruct AMPL to solve each problem instance using the same model. Answer the following questions using information obtained from the optimal solutions.
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