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simplex_examples

# simplex_examples - Lec6 class example(slide 11 Phase 1...

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Lec6 class example (slide 11) Phase 1 iteration 1 z x1 x2 s1 e1 a1 a2 Name step size -30.00 -2.00 -4.00 0.00 1 0 0 Row0 s1 4.00 0.50 0.25 1.00 0.00 0.00 0.00 Row1 16.00 a1 20.00 1.00 3.00 0.00 -1.00 1.00 0.00 Row2 6.67 a2 10.00 1.00 1.00 0.00 0.00 0.00 1.00 Row3 10.00 Not: Phase 1 objective function is minimize a1 + a2. Basis is s1,a1,a2. Row0 coefficient for basic variables are 0; coefficient for non basic are reduced cost, cj - cB(B^-1)Aj. Recall that each column j in the table is equal to (B^-1)Aj After calculating the reduced costs (row0), x2 is decided to be the entering variable, a1 is the leaving variable (min pivot) x2 should replace a1 in the basis, therefore column for x2 should be (0,0,1,0). Use row operations to get that. Phase 1 iteration 2 z x1 x2 s1 e1 a1 a2 Name step size -3.33 -0.67 0.00 0.00 -0.33 1.33 0.00 Row02 s1 2.33 0.42 0.00 1.00 0.08 -0.08 0.00 Row12 5.60 x2 6.67 0.33 1.00 0.00 -0.33 0.33 0.00 Row22 20.00 a2 3.33 0.67 0.00 0.00 0.33 -0.33 1.00 Row32 5.00 Not: To get this table: First, [Row2]/3, second: [Row3]-[Row2]/3, third:[Row1]-[Row2]/3*0.25, fourth: [Row0]+[Row2]/3*4 x1 is decided to be the entering variable, a2 is the leaving variable (min pivot).

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