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initialzn_calc - Phase I system The initial Simplex tableau...

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Phase I system The initial Simplex tableau is: x1 x2 x3 x4 x5 x6 x7 x8 rhs ------------------------------------------------- 1 1 1 1 0 0 1 0 100 0.9 0.3 -0.6 -1 -1 0 0 1 0 0.2 0.1 0 -0.3 0 1 0 0 0 ------------------------------------------------- (-w) 0 0 0 0 0 0 1 1 0 To get a tableau w.r.t. B = (7,8,6) we need to subtract 1st 2 rows from (-w) row. subtract 1st row from (-w) row x1 x2 x3 x4 x5 x6 x7 x8 rhs ------------------------------------------------- 1 1 1 1 0 0 1 0 100 0.9 0.3 -0.6 -1 -1 0 0 1 0 0.2 0.1 0 -0.3 0 1 0 0 0 ------------------------------------------------- (-w) -1 -1 -1 -1 0 0 0 1 -100 subtract 2 nd row from (-w) row x1 x2 x3 x4 x5 x6 x7 x8 rhs --------------------------------------------------- 1 1 1 1 0 0 1 0 100 0.9 0.3 -0.6 -1 -1 0 0 1 0 0.2 0.1 0 -0.3 0 1 0 0 0 --------------------------------------------------- (-w) -1.9 -1.3 -0.4 0 1 0 0 0 -100 Now we have the Phase I tableau for B = (7,8,6): Since we are minimizing column 1 looks good, tie for min ratio, can pivot in row 2 or 3. Gaussian elimination with pivot = row 2, column 1. The resulting tableau is: x1 x2 x3 x4 x5 x6 x7 x8 rhs --------------------------------------------------------------- 0 0.667 1.67 2.11 1.11 0 1 -1.11 100 1 0.333 -0.667 -1.11 -1.11 0 0 1.11 0 0 0.0333 0.133 -0.0778 0.222 1 0 -0.222 0 --------------------------------------------------------------- (-w) 0 -0.667 -1.67 -2.11 -1.11 0 0 2.11 -100 Column 4 looks good, must pivot in row 1 Gaussian elimination with pivot = row 1, column 4.
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