
EXAMPLE OF SIMPLEX PROCEDURE
FOR A NONSTANDARD
LINEAR PROGRAMMING PROBLEM 


Below is
original
Problem 


Red symbols
below were
changed by
step NS1 


Red variables s_{n}
below are called
SLACK VARIABLES 


There is a tie
for most negative
righthand number.
Either "12" is OK 


In the matrix
below, the
pivot has
become "1" 

Named below are the 4
row operations needed
to pivot on the number
"2" encircled in red 


Row operations
are named above;
their results
are below 
Highlighted
is the
new ISM 


In the matrix
below, the
pivot has
become "1" 

Named below are the 4
row operations needed
to pivot on the number
"3/2" encircled in red 



Row operations are named above; their
results are at the right. The new ISM is highlighted. All rightmost numbers above the
bottom (objective) row are now zero or bigger;
Phase I is now ended.
Phase II now begins, presented as "Step 8" in Rolf (Pg 323) 



In many nonstandard problems, we would now find a negative indicator in
the bottom row. However, in our last tableau above, a nice coincidence finds
all indicators (0, 0, 0, 4/3, 1/3) are zero or bigger; "20" is not an
indicator. Hence, Phase II is completed at it's start, because the above tableau is a
final tableau, and the row operations of SIMPLEX are done!
To obtain the final basic solution to our problem,
1^{st} set equal to 0 each variable NOT associated
with the highlighted ISM: variable tags are placed
above each column in the final tableau.
2^{nd}
convert each row of the final tableau back
into it's equation format, as at the right, to find the
values of the remaining variables (shown in red). 

