Principles of Mathematics in Operations Research

8.2 Simplex Tableau

cTN-cTBB~xN = [2 0] - [0 3

cTN-cTBB~lN= [2 0] - [0 3]

]

-12'

0 1

"3-2'

2 -1

[l Ol

2-1

( X Z2

v-4 3

Since the first component is negative, P is not optimal; x should enter the

basis, i.e.

x,Ne = => B^N' = ,B_16 =

Zl

y

=

6

6 -

3

2

x>

0

0

xB = B-^1 b-B-^1 Nexe

a = Min{l = 2, § = 3} = 2. Thus, xL = zuxe = 2,y = Q-2a = 2.

xB

_XN _

"2'

2

U

0

X

y

Zl

.Z2.

4 = [B\N] =

cT=[cT\cl] = [2 3\0 0],B =

[5|/] = n

c£-c££-^1 JV = [0 0] - [2 3]

12

2 1

-1 0

0-1

1 2

2 1

10

01

1 2

0-3

10

-2 1

->•

1 2

2 1

1 Ol —^ ^

1 ul 3 3

Oil ^ _I U 1I 3 3

[J|*-l].

I I

I -I

-1 0

0-1

00 23

1 _2

3 3

2 _1

"3 3

H]>«-

77ms, extreme point Q in Figure 8.1 is optimal, c^B xb = 10 is the optimal

value of the objective function.

8.2 Simplex Tableau

We have achieved a transition from the geometry of the simplex method to
algebra so far. In this section, we are going to analyze a simplex step which
can be organized in different ways.
The Gauss-Jordan method gives rise to the simplex tableau.

[A\\b] = [B\N\\b] —• [IIB^NWB-H].