
THE ZCOLUMN IN SIMPLEX METHOD MATRICES 

An important early step in SIMPLEX METHOD is the creation of the SIMPLEX
TABLEAU. Below is a problem from another exercise, and the simplex tableau derived from it:
MAXIMIZE 
z = x_{1} + 2x_{2} + 3x_{3} 
SUBJECT TO : 
2x_{1} + x_{2} + x_{3} 4 
4x_{1} + 2x_{2} + 3x_{3} 3 
x_{1}0; x_{2}0; x_{3}0 



The red zCOLUMN is included in our text as a device to find the value of z
at basic solutions (i.e., corner points).
If the ZCOLUMN is visible (above), we find z (at each basic solution) by
converting the bottom (objective) row into equation form.
However, during the row operations of the SIMPLEX METHOD, this zCOLUMN
never changes, and therefore Prof McFarland chooses to omit it to save time
and space, and to simplify the appearance of tableaus. Any student may
either keep or omit this zCOLUMN: the row operations will be unaffected
whichever you choose. The omission of a zCOLUMN has one cost: we must
remember that in all simplex tableaus, the value of z is found in the lower
right corner.



This page last updated
23 June 2007 
