Week 9

Week 9 - Examples of the Simplex Algorithm EE103 Winter09...

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Examples of the Simplex Algorithm EE103 Winter09 TA Discussion Session Ni-Chun Wang
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12 max 2 .. 2 2 33 ,0 xx st x x + +≤ c T = (1,2) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 X 1 X 2 x 1 +3x 2 3 2x 1 +x 2 2 Example 1
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12 max 2 .. 2 2 33 ,0 xx st x x + +≤ 1 2 2 2( ) 0 z x x v v z + += + + +− = 0 01 T AI c 0 b ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ x v z [Fact] (m+1) equations, (n+m+1) unknown variables => infinite number of solutions !
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12 max 2 .. 2 2 33 ,0 xx st x x + +≤ 1 2 2 2( ) 0 z x x v v z + += + + +− = 0 01 T AI c 0 b ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ [] 00; [ 23 ] , 0 T T one obvious feasible solution is x v z = =− = x v z There is always an identity matrix embedded in the tableau.
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0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 X 1 X 2 x 1 +3x 2 3 2x 1 +x 2 2 c T = (1,2)
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12 22 20 33 0 vx = −≥ = stronger constraint objective coefficients fix x 1 =0 and increase x 2 21 2 xv += 2 1. We want x = Perform complete Gauss Elimination on (2,2) element of T0 2 2 2 1 x x
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[] 01 ; [1 0 ], 2 T T one obvious feasible solution is x v z = =− = identity matrix 1 2 1 1 v x = = 1 2 0 0 x v = =
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0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 X 1 X 2 x 1 +3x 2 3 2x 1 +x 2 2 c T = (1,2)
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This note was uploaded on 03/30/2009 for the course EE 103 taught by Professor Vandenberghe,lieven during the Winter '08 term at UCLA.

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Week 9 - Examples of the Simplex Algorithm EE103 Winter09...

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