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Unformatted text preview: OR&IE 320/520 10/16/07 Prof. Bland Initialization of the Simplex Method: An Example Using Ar tificial Variables cf. BHM Chapter 2 sections 2,4,5. Recall (from Rec Exercise/Problem Set 4) the AluMinimum Corp. problem concern ing the production of a lowcost aluminum alloy from scrap (recycled beer cans). For the current production period AluMinimum Corp has orders for 100 tons of an alloy that must contain at least 1% silicon and at most 1% manganese . There are four sources of scrap aluminum available (in plentiful supply). The ta ble below shows the cost per ton (including processing costs) and the silicon and manganese content for each of the four kinds of scrap. Scrap 1 Scrap 2 Scrap 3 Scrap 4 Cost (US dollars per ton) 350 300 250 200 Percentage Silicon 1.9 1.3 .4 Percentage Manganese 1.2 1.1 1 .7 We came up with the following linear programming formulation: minimize 350 x 1 + 300 x 2 + 250 x 3 + 200 x 4 subject to: 1 x 1 + 1 x 2 + 1 x 3 + 1 x 4 = 100 . 9 x 1 + . 3 x 2 + . 6 x 3 + 1 x 4 ≥ . 2 x 1 + . 1 x 2 + x 3 + . 3 x 4 ≤ x 1 ≥ , x 2 ≥ , x 3 ≥ , x 4 ≥ . We produced AMPL model and data files for this problem and solved it using AMPL. But I am wondering how AMPL got started. In some of our examples (e.g., making beer and sausages) it was easy to get an initial feasible simplex tableau, because the...
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This note was uploaded on 03/30/2008 for the course ORIE 320 taught by Professor Bland during the Fall '07 term at Cornell.
 Fall '07
 BLAND

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