I'm trying to look at how the Simplex method in standard form works. I understand the basics of how ti works, but I can't understand what happens between two steps.
I'm using the example from chapter 6 of Seymour Lipschutz's book Schaum's Outline of Finite Mathematics. The formulas I'm trying to maximize:
$$ x+y+z+u=3 $$ $$ 2x+2y+z+v=4 $$ $$ x-y+w=1 $$ $$ -4x+2y+z+f=0 $$
I understand how to create the initial tableau, which is:
I can follow the steps to get the pivot entry (the $1$ in the $w$ row and $x$ column) and I can follow most of the steps to get the next tableau, however some entries seem to change with no explanation. The steps I'm following are:
- Divide each entry in the row of the pivot by the pivot entry
- In all other rows, introduce a zero in the column of the pivot entry
- Replace the variable label to the left of the pivot by the variable label above the pivot
After following this you're meant to get:
The first and third steps I'm fine with. I think the problem I'm having is with the second step. I can't see why the other values in the $u$, $v$ and $f$ rows change. Any pointers on what I'm missing?
This is a repost from CS Theory