Suppose a problem is in canonical form and the associated basic feasible solution is degenerate, and $x_1$ is a basic variable with the value zero. The pivot operation is performed with the $x_1$ variable extracted from the basis. Describe the new basic feasible solution.

I am learning the Linear Programming by self-study. I didn't understand this problem and didn't know what the new basic feasible solution is.

  • $\begingroup$ Hint: In the dictionary (or tableau depending on the notation that you're using) that results from this pivot, what's the value of the new basic variable? What happens to the values of the remaining basic and non-basic variables? $\endgroup$ – Brian Borchers Sep 19 '16 at 23:40
  • $\begingroup$ @BrianBorchers One Non-basic variable become a new basic variable with the value non-zero? I still didn't know how to do and understand this problem. Can you give me more hints? $\endgroup$ – User90 Sep 20 '16 at 2:20
  • $\begingroup$ You really don't seem to understand what the terms in this problem mean, so I'm afraid that you're going to have a very hard time completing your homework. $\endgroup$ – Brian Borchers Sep 20 '16 at 4:10
  • $\begingroup$ @CZX If you can point us to an image of your initial tableau and the tableau after your first pivot, then I can explain more easily. $\endgroup$ – tomi Sep 20 '16 at 23:01
  • $\begingroup$ @tomi This is the original problem. There are no initial tableau. (。•́︿•̀。) $\endgroup$ – User90 Sep 21 '16 at 1:06

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