Week 10

# Week 10 - Simplex Algorithm(2 EE103 Winter09 TA Discussion...

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Simplex Algorithm (2) EE103 Winter09 TA Discussion Session Ni-Chun Wang

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3 12 3 3 3 20 12 10 min 8 32 17 3 9 8 2 16 0 x xx x x x x −+ ++ Example 123 1 3 2 3 3 3 1234 min .. 3 2 8 17 3 9 2 8 + 16 12 10 20 ( ) 0 ,,, 0 z st x x x v x v x v x z x x + = + = + += + =
123 1 12 3 2 3 3 3 1234 max .. 3 2 8 17 3 9 2 8 + 16 12 10 20 ( ) 0 ,,, 0 z st x x x v xx x v x v x z x x + ++ = + = + += −+ + = 1 x 2 x 3 x 1 v 2 v 3 v z [] 000 ; [17 19 16] , 0 T T one obvious feasible solution is x v z = =− =

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1 x 2 x 3 x 1 v 2 v 3 v z 1. Find the most NEGATIVE objective function coefficients (minimization problem) 2. Increase x 3 while keep x 1 x 2 =0 3 17 /8 x 3 9/3 x 3 16/8 x strongest constraint 3. row 3 gives the strongest constraint / increase x 3 => pivot on (3,3) minimum ratio test
1 x 2 x 3 x 1 v 2 v 3 v z [] 002 ; [1 3 0] , 40 T T one obvious feasible solution is x v z = =− =

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1 x 2 x 3 x 1 v 2 v 3 v z [] 002 ; [1 3 0] , 40 T T one obvious feasible solution is x v z = =− = 1. increase x 1 while keep x 2 , v 3 =0 2. row 1 gives the strongest constraint on x 1 3. pivot on (1,1)
1 x 2 x 3 x 1 v 2 v 3 v z [] 1 0 1.75 ; [0 2.75 0] , 47 T T one obvious feasible solution is x v z = =− =

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Week 10 - Simplex Algorithm(2 EE103 Winter09 TA Discussion...

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