Tell the pivot row and the pivot column of the following simplex tableau: $\begin{bmatrix} 1 & 2 & 10 & 1 & 0 & 0 & | & 40 \ 3 & -2 & 2 & 0 & 1 & 0 & | & 20 \ -90 & -100 & -80 & 0 & 0 & 1 & | & 0 \end{bmatrix}$ Choices may be used once, more than once, or not at all. 1. 1 2. 2 3. 3 The pivot COLUMN would be column #____ 4. 4 The pivot ROW would be row #____ 5. 5 6. 6 7. 7
Added by Dennis N.
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The pivot element is typically chosen as the most negative value in the bottom row (excluding the last column). In this case, the most negative value in the bottom row is -100. To find the pivot column, we need to identify the column that corresponds to the Show more…
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Pivot once as indicated in each simplex tableau. Read the solution from the result. $$ \begin{array}{rrrrrrr|r}{x_{1}} & {x_{2}} & {x_{3}} & {x_{4}} & {s_{1}} & {s_{2}} & {s_{3}} & {z} \\ {1} & {2} & {3} & {1} & {1} & {0} & {0} & {0} & {115} \\ {2} & {1} & {8} & {5} & {0} & {1} & {0} & {0} & {200} \\ {1} & {0} & {1} & {0} & {0} & {0} & {1} & {0} & {50} \\ \hline-2 & {-1} & {-1} & {-1} & {0} & {0} & {0} & {1} & {0}\end{array} ] $$
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Pivot once as indicated in each simplex tableau. Read the solution from the result. $$ \begin{array}{rrrrrr|r}{x_{1}} & {x_{2}} & {x_{3}} & {s_{1}} & {s_{2}} & {s_{3}} & {z} \\ {4} & {2} & {3} & {1} & {0} & {0} & {0} & {22} \\ {2} & {2} & {5} & {0} & {1} & {0} & {0} & {28} \\ {1} & {3} & {2} & {0} & {0} & {1} & {0} & {45} \\ \hline-3 & {-2} & {-4} & {0} & {0} & {0} & {1} & {0}\end{array} ] $$
Pivot once as indicated in each simplex tableau. Read the solution from the result. $$ \left[\begin{array}{rrrrrr|r}{x_{1}} & {x_{2}} & {x_{3}} & {s_{1}} & {s_{2}} & {s_{3}} & {z} \\ {2} & {2} & {1} & {1} & {0} & {0} & {0} & {12} \\ {1} & {2} & {3} & {0} & {1} & {0} & {0} & {45} \\ {3} & {1} & {1} & {0} & {0} & {1} & {0} & {20} \\ \hline-2 & {-1} & {-3} & {0} & {0} & {0} & {1} & {0}\end{array}\right] $$
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