If so, why?
If not, do they differ by some ERO/s? That is, they are row equivalent?
This is the problem (taken from Chapter 2 here):
My classmate gave an optimal tableau that is different from the one obtained by both the computer and myself:
I solved the following (here):
$$\text{Maximize }z = 3x_1 + x_2 + 3x_3$$
Subject to:
$$2x_1 + x_2 + x_3 \le 2$$
$$x_1 + 2x_2 + 3x_3 \le 5$$
$$2x_1 + 2x_2 + x_3 \le 6$$
The computer and I got:
or
While the tableaus are different, my classmate, the computer, and I have the same optimal solution of
$$z = \frac{27}{5};\text{ }x_1 = \frac{1}{5}, x_2 = 0, x_3 = \frac{8}{5}$$
Is it possible that both tableaus are correct? If so, can one be obtained from the other through EROs? Is there some kind of theorem for this? Optimal tableaus are row equivalent or something like that?