a Simplex
EXAMPLE OF SIMPLEX PROCEDURE
FOR A STANDARD
LINEAR PROGRAMMING PROBLEM

Below is the
original problem:
objective function
is in green.
See
step
1
Red variables below
are called
SLACK VARIABLES
See
step
2
Below is the
SIMPLEX TABLEAU.
Compare RED symbols
with Z = x1 + 2x2 - x3.
Highlighted below
is the "ISM".


The 1st SIMPLEX TABLEAU
is below. (credit Steve Hulet) Note
missing z-column
Highlighted is the "ISM"
See steps 3,4,5 of
SIMPLEX METHOD
as you handle INDICATORS,
RATIOS, and PIVOTS.
Named below are the 4
row operations needed to
pivot on the number
"5" encircled in red

Below are the
results of the
row operations
named above
highlighted
is the
new ISM
Since one INDICATOR
(namely -1/5) remains
negative, we must
repeat steps 3-9
Below is the result
of changing our pivot
to "1"
Named below are
4 row operations
needed to pivot
on the number(16/5)
encircled in red
Above there was a tie for least non-negative ratio:
either row 1 or row 2 could have become the pivot row, and either choice leads to the final tableau after one additional pivoting. At the right is the result of the final 3 row operations. "ISM" is highlighted
    
All indicators {0, 0, 49
16
, 0,  1 
16
and 3
8
} are now zero or bigger ("13" is NOT an indicator).
Thus, as in step 8 of the SIMPLEX METHOD, the last tableau is a FINAL TABLEAU.
Row operations of SIMPLEX METHOD are done.
Thus, the basic solution for the tableau above is the solution to our original problem.
[1st] set equal to 0 all variables NOT associated with the above highlighted ISM. The columns of the final tableau have variable tags.
[2nd] convert each row of the final tableau (except the bottom row) back into equation form (as at the right) to find the values of the remaining variables. The value of the objective function is in the lower right corner of the final tableau.

  
This page last updated
6 March 2016