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# sol5 - AMS 540 MBA 540(Fall 2010 Estie Arkin Homework Set 5...

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AMS 540 / MBA 540 (Fall, 2010) Estie Arkin Homework Set # 5: Solution notes 1). (a). z x 1 x 2 x 3 x 4 x 5 x 6 RHS 1 2 3 -1 -12 0 0 0 0 -2 -9 1 9 1 0 0 0 1/3 1 -1/3 -2 0 1 0 x 2 enters, x 6 leaves (only competitor in the min ratio test): z x 1 x 2 x 3 x 4 x 5 x 6 RHS 1 1 0 0 -6 0 -3 0 0 1 0 -2 -9 1 9 0 0 1/3 1 -1/3 -2 0 1 0 x 1 enters, x 5 leaves (favor first row when we have a tie in min ratio test): z x 1 x 2 x 3 x 4 x 5 x 6 RHS 1 0 0 2 3 -1 -12 0 0 1 0 -2 -9 1 9 0 0 0 1 1/3 1 -1/3 -2 0 x 4 enters, x 2 leaves (only competitor in the min ratio test). z x 1 x 2 x 3 x 4 x 5 x 6 RHS 1 0 -3 1 0 0 -6 0 0 1 9 1 0 -2 -9 0 0 0 1 1/3 1 -1/3 -2 0 x 3 enters, x 1 leaves (favor first row when we have a tie in min ratio test): z x 1 x 2 x 3 x 4 x 5 x 6 RHS 1 -1 -12 0 0 -2 -3 0 0 1 9 1 0 -2 -9 0 0 -1/3 -2 0 1 1/3 1 0 x 6 enters, x 4 leaves (only competitor in the min ratio test). z x 1 x 2 x 3 x 4 x 5 x 6 RHS 1 0 -6 0 -3 1 0 0 0 -2 -9 1 9 1 0 0 0 -1/3 -2 0 1 1/3 1 0 x 5 enters, x 3 leaves, (favor first row when we have a tie in min ratio test) and we get the initial tableau again. (b). I will use the lex method, entering the variable with max z j c j . The first pivot is as in part (a), x 2 enters,

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