Previous table of simplex algorithm I have this problem of simplex method which shows cycle . 
Problem : Maximize $Z=10x_1-57x_2-9x_3-24x_4$
Constraint to : 
           $ 0.5x_1-5.5x_2-2.5x_3+9x_4<=0 $,
           $ 0.5x_1-1.5x_2-0.5x_3+x_4<=0 $,$ x_1<=1 $
I know that next table of this problem can be found by gaussian method . But how can I found previous table ? 
So far I have received a comment from an user . What is meant here by previous table ? To clarify this statement, Look at the following : 
Maximize $p = (1/2)x + 3y + z + 4w$ subject to
$x + y + z + w <= 40$
,$2x + y - z - w >= 10$,
$w - y >= 10$
Here in the image I have given two iterations in tabular format . Table 1 is the previous table of table 2 . So hope the language clarification is okay . 

 A: I do not believe this is possible due to the information loss that necessarily takes place at each step of the simplex algorithm.
Recall that the purpose of a step of the simplex algorithm is to improve the current solution by selecting a variable to enter to the basis (in other words $\gt 0$), increasing its value to the point where one of the existing variables has to leave the basis (i.e, $=0$). For instance, in the example you've added, $x$ has entered and $s_2$ has exited the basis. Each new tableau represents a different, but equivalent expression of the optimization problem. Gauss-Jordan elimination operations are used to perform this pivoting process.
There are several ways that this process irreversibly eliminates information:


*

*The entering variable/pivoting column is typically selected based on which element in the bottom row has the smallest (i.e., most negative) value. (I notice you did not use this criterion in your example, for some reason.) Once the pivot is complete, this value will be zero---as are the values corresponding to the other basic variables. There is no way tell which of the basic variables is "newest" simply by looking at the bottom row.

*Once a pivot row is selected---typically the row with the smallest ratio between the right-hand column and the pivot column---the row is normalized so that the pivot value is 1. For instance, in your example, the second row was divided by 2. There is no way to tell after the what this scaling was, so you cannot recover the original values of the pivot row.

*The normalized pivot row is subtracted from each of the other rows to zero out the other elements of the pivot column. For instance, in your example, the scales for rows 1, 3, and 4 are -1, 0, and +0.5, respectively. Once the subtraction is complete, there is no way to know what those scales were. So you cannot recover the original values of the non-pivot rows.


Hopefully it's clear, then, that the simplex algorithm is not a reversible process. Information is lost at every step in the progress towards a solution. You can't even determine what the original model was simply by looking at an intermediate tableau.
