I'm working through the examples in my professor's class notes, but I can't figure out how to solve this problem:
Example: In the following standard tableau, mark by * the choices for the pivot entry consistent with the simplex method: (Note last row is the objective function)
$$ \begin{array}{|ccccc|c|} \hline x_1&x_2&x_3&x_4&x_5&-1&\\ \hline 0&1&-2&3&4&2&=-x_6\\ 1&1&-2&3&4&0&=-x_7\\ -3&-1& 0&-3&-4&-2&=-x_8\\ \hline 1&1& 2&1&1&-1&\rightarrow max\\ \hline \end{array} $$
Solution.
$$ \begin{array}{|ccccc|c|} \hline x_1&x_2&x_3&x_4&x_5&-1&\\ \hline 0&1&-2&3*&4&2&=-x_6\\ 1*&1*&-2&3&4*&0&=-x_7\\ -3&-1& 0&-3*&-4&-2&=-x_8\\ \hline 1&-1& -2&1&1&-1&\rightarrow max\\ \hline \end{array} $$
I just don't know how these pivots are being identified. I might just be misunderstanding the question, because I thought that each step of the simplex method only had one possible pivot point.
Thanks for the help!