Principles of Mathematics in Operations Research

8.2 Simplex Tableau 109

:J-:0---0

: /

0:0---0

*•••*: 1

B~lN\ '•.B~lN

• :ce — Cnv: •

B-lb

-dB^b

For all the rows except the objective function row, do the following oper-

ation. For row i, multiply Vi*(the updated first row) and subtract from row

i. For the objective function row, multiply the first row by (ce — CBTV) and

subtract from the objective function row.

What we have at the end is another simplex tableau.

:0---0

_Vj_

,~Ce cgV.Q.. .Q

:0

:0

*•••*: 0 :*••• *

a

—c^B^1 b — a(ce — CgV BU) A

Example 8.2.1 The starting tableau at point P is

A b

=rllo

B\N\\b

rCT\rT\\()

B\CN\\U

=

"-1 2

01

03

1 0

2-1

2 0

6"

6

0

The final tableau after Gauss-Jordan iterations is

Zl

y

z

zi y

1 0

0 1

00

X Zi

3-2

2 -1

-4 3

RHS~

6

6

-18

=

B-XN \B~lb

0\rT

v\cN

c^^JVll -cost

Since the reduced cost for x is — 4 < 0, x should enter the basis. The
minimum ratio a = Mm{|, |} = 2 due to z\, thus z\ should leave the basis.