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Lecture 9C - Simplex Algorithm Toward Efficient Computation...

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EE103 Lec 9C (SEJ) 1 Simplex Algorithm: Toward Efficient Computation max 4 9 7 10 0 = 6 5 1 2 3 4 3 40 0 4 ( ) 1 2 3 4 6 0 z x x x x x z x x x x x z T + + + + + + + + + + = 12 20 18 40 0 0 0 5 1 2 3 4 6 0, 1,...,6 x x x x x x z x i i + + + + + = = 1 2 3 4 5 6 7 0 4 9 7 10 1 0 0 6 1 1 3 0 1 0 4 12 20 18 40 0 0 1 0 40 a a a a a a a b T = 0 0 0 3x3 0 1 T z B B B I c = = 5 6 0 2x2 [ , ] B a a I = = 0 5 6 ( , ) (0,0) T B c c c = = 1 5 4 1 1 0 [ , ] 0 1 (0,40) 1 T z B B a a B c = = 1 1 1 1 1 1 1 0 1 z T B B B c B = 1 1 1 0 1 1 1 (2,4) 0 1 T B the pivot on B T T c B = EE103 Lec 9C (SEJ) 2 Simplex Algorithm: Toward Efficient Computation 1 2 3 4 5 6 7 0 4 9 7 10 1 0 0 6 1 1 3 0 1 0 4 ( ) 12 20 18 40 0 0 1 0 40 a a a a a a a b T Original data = 1 5 4 1 1 0 [ , ] 0 1 (0,40) 1 T z B B a a B c = = 1 1 1 1 1 1 1 0 1 z T B B B c B = 1 1 1 0 1 1 1 (2,4) 0 ( ?) 1 T B the pivot on B T T why c B = 1 2 3 4 5 6 7 1 1 0 1 8.75 6.25 0 1 0.25 0 5 0.025 0.025 0.075 1 0 0.025 0 0.1 11 19 15 0 0 1 .75 1 4 3 z a a a a a a a b B T T = =
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