sol10 - CO350 Homework 10 Solutions - Winter 2007 1. 11.4.1...

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CO350 Homework 10 Solutions - Winter 2007 1. 11.4.1 (a) Gomory cuts z -row: 5 / 12 x 4 + 1 / 12 x 5 + 5 / 12 x 6 1 / 4 x 3 -row: 11 / 60 x 4 + 11 / 12 x 5 + 59 / 60 x 6 3 / 4 x 2 -row: 1 / 10 x 4 + 1 / 2 x 5 + 9 / 10 x 6 1 / 2 x 1 -row: 1 / 12 x 4 + 5 / 12 x 5 + 1 / 12 x 6 1 / 4 (b) New constraints and dual pivots z -row: - 5 / 12 x 4 - 1 / 12 x 5 - 5 / 12 x 6 + s 1 = - 1 / 4, s 1 leaves, x 5 or x 6 enters x 3 -row: - 11 / 60 x 4 - 11 / 12 x 5 - 59 / 60 x 6 + s 2 = - 3 / 4, s 2 leaves, x 5 enters x 2 -row: - 1 / 10 x 4 - 1 / 2 x 5 - 9 / 10 x 6 + s 3 = - 1 / 2, s 3 leaves, x 5 enters x 1 -row: - 1 / 12 x 4 - 5 / 12 x 5 - 1 / 12 x 6 + s 4 = - 1 / 4, s 4 leaves, x 5 enters (c) New constraints in terms of the original variables z -row: 3 x 1 - 2 x 2 + 2 x 3 4 x 3 -row: 7 x 1 - 4 x 2 2 x 2 -row: 6 x 1 - 4 x 2 1 x 1 -row: x 1 7 / 6 2. 11.4.2 The first tableau for the relaxed LP is: z + x 1 - 3 x 2 = 0 x 1 - x 2 + x 3 = 2 2 x 1 + 4 x 2 + x 4 = 15 Entering variable: x 2 Leaving variable: x 4 Pivoting gives the optimal tableau:
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This note was uploaded on 02/21/2010 for the course CO 350 taught by Professor S.furino,b.guenin during the Winter '07 term at Waterloo.

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sol10 - CO350 Homework 10 Solutions - Winter 2007 1. 11.4.1...

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