If there is a zero in the bottom row of a column that is not a unit column, then we may have infinite solutions.
We start by finding the optimal solution from the current tableau (the one with a zero in the bottom row of a column that is not a unit column).
We then pivot on the non-unit column with a zero in the bottom row. We pivot on the row with the smallest non-negative test ratio.
The new tableau will give the same optimal value at a different point.
We continue finding additional points as needed.
All points on the segment(s) connecting the points are solutions.
Remember, there are two ways we can have no solution.
No Feasible Region: If the simplex tableau has a negative entry in the last column but no other entries in that row are negative, then there is no feasible region. (So, there is no solution.)
Unbounded: If the simplex tableau has no positive entries in the pivot column, then the feasible region is unbounded. (So, there is no maximum value, which means there is no solution.)