ofparam - ORIE 3300/5300 Prof. Bland Fall 2011 Objective...

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Unformatted text preview: ORIE 3300/5300 Prof. Bland Fall 2011 Objective Function Parametrics Initial Tableau x2 x3 x4 30 40 0 2 5 1 −z 1 0 x1 20 2 0 4 2 1 0 3 6 6 x5 0 0 x6 0 0 0 80 0 1 0 120 0 0 1 210 Treat c3 as a parameter, and examine z ∗ (c3 ). −z 1 x1 0 x2 0 0 0 0 0 x4 -5 x5 0 x6 − 10 3 -1100 1 x3 -45 c3 −1 2 1 −2 0 1 3 30 1 0 3 1 0 1 −3 10 0 0 -10 -3 1 2 3 20 Optimal for c3 ≤ 45. At c3 = 45+ pivot x3 in and x1 out. −z 1 x1 15 − c33 x2 0 x3 0 0 1 6 1 0 x4 10 − c33 −1 3 x5 0 x6 − 25 3 + c93 0 5 18 0 1 3 0 1 1 3 0 1 −9 3 1 3 0 10 3 0 0 1 3 1 4 −9 53 1 3 Optimal for 45 ≤ c3 ≤ 75. At c3 = 75+ pivot x6 in and x2 out. 1 -950 − 10c3 3 2 31 3 −z 1 x1 x2 20 30 −.4c3 −.4c3 x3 0 x4 0 −.2c3 6 0 −5 x5 0 x6 0 0 −16c3 1 114 0 3 5 18 5 0 2 5 2 5 1 1 5 0 0 16 0 18 5 8 5 0 −1 5 1 0 104 Optimal for c3 ≥ 75. Give z ∗ (c3 ) and x∗ (c3 ) for all c3 . 2 ...
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