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Unformatted text preview: CO350 Linear Programming Chapter 7: The TwoPhase Method 16th June 2005 Chapter 7: The TwoPhase Method 1 Recap To construct auxiliary problem ( A ) for ( P ) max c T x s.t. Ax = b x we make sure that b , introduce one artificial variable u i for each constraint, and change the objective to m X i =1 u i . After solving ( A ) , if ( A ) has optimal value < , ( P ) is infeasible; if ( A ) has optimal value = 0 , we can get a feasible basis for ( P ) from the optimal tableau for ( A ) . Chapter 7: The TwoPhase Method 2 Infeasibility ( 7.2) Example of infeasibility Given the LP problem ( P ) max ( z =) x 1 s.t. 3 x 1 + 5 x 2 + 2 x 3 x 4 = 7 2 x 1 + 5 x 2 + 3 x 3 + x 4 = 3 x 1 , x 2 , x 3 , x 4 The auxiliary problem is ( A ) max ( w =) x 5 x 6 s.t. 3 x 1 + 5 x 2 + 2 x 3 x 4 + x 5 = 7 2 x 1 + 5 x 2 + 3 x 3 + x 4 + x 6 = 3 x 1 , x 2 , x 3 , x 4 , x 5 , x 6 Tableau corresponding to B = { 5 , 6 } is w 5 x 1 10 x 2 5 x 3 = 10 3 x 1 + 5 x 2 + 2 x 3...
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This note was uploaded on 06/11/2011 for the course C 350 taught by Professor Wolkowicz during the Fall '97 term at Waterloo.
 Fall '97
 Wolkowicz

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