rhsparam - 10 57-. 35 b 1 1 1 10 3 10-2 15 8 + . 1 b 1 1 3...

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OR 320/520 Optimization I 10/9/07 Prof. Bland Right-hand-side Parametrics We will return to the sausage-making example and use it to illustrate para- metric analysis of z * ( b i ). In this example we take the Frst right-hand-side value b 1 to be the parameter, and analyze z * ( b 1 ) for all b 1 0. Note that in this handout I have dropped the z -column from the tableau. Initial Tableau x 1 x 2 x 3 x 4 x 5 x 6 20 30 40 0 0 0 0 2 2 5 1 0 0 80 4 2 1 0 1 0 120 3 6 6 0 0 1 210 1 ± x 1 x 2 x 3 x 4 x 5 x 6 0 0 -5 -5 0 - 10 3 - 700 - 5 b 1 0 1 - 1 2 - 1 2 0 1 3 70 - b 1 / 2 1 0 3 1 0 - 1 3 - 70 + b 1 0 0 -10 -3 1 2 3 260 - 3 b 1 Optimal for 70 b 1 86 2 3 . At b 1 = 70 - pivot x 1 out and x 6 in (see tableau 2). At b 1 = 86 2 3 + pivot x 5 out and x 3 in (see tableau 3).
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2 ± x 1 x 2 x 3 x 4 x 5 x 6 -10 0 -35 -15 0 0 - 15 b 1 1 1 5 2 1 2 0 0 b 1 / 2 -3 0 -9 -3 0 1 210 - 3 b 1 2 0 -4 -1 1 0 120 - b 1 Optimal for 0 b 1 70. 3 ± x 1 x 2 x 3 x 4 x 5 x 6 from 1 ± 0 0 0 - 7 2 - 1 2 - 11 3 - 830 - 7 2 b 1 0 1 0 - 7 20 - 1 20 3
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Unformatted text preview: 10 57-. 35 b 1 1 1 10 3 10-2 15 8 + . 1 b 1 1 3 10-1 10-2 30-26 + . 3 b 1 Optimal for 86 2 3 b 1 57 . 35 162 . 86. At b 1 = 57 . 35 + pivot x 2 out, and x 4 (or x 5 ) in (see tableau 4). 4 x 1 x 2 x 3 x 4 x 5 x 6-10-20 3-1400 1-162 . 857 + b 1 1 24.286 1 22.857 Optimal for 57 . 35 b 1 . Now give z * ( b 1 ) for all b 1 0, and plot z * versus b 1 . Also give x * ( b 1 ) for all b 1 0....
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rhsparam - 10 57-. 35 b 1 1 1 10 3 10-2 15 8 + . 1 b 1 1 3...

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