A =

1 2 -1 1 1 0 0 0

2 -2 3 3 0 1 0 9

1 -1 2 -1 0 0 1 6

-4 1 -4 -3 0 0 0 -15

the pivot element is the element

1 1

1 2 -1 1 1 0 0 0

0 -6 5 1 -2 1 0 9

0 -3 3 -2 -1 0 1 6

0 9 -8 1 4 0 0 -15

here is the basic elements index

1 6 7

and here is the non-basics.....

5 2 3 4

the pivot element is the element

2 3

1.0000 0.8000 0 1.2000 0.6000 0.2000 0 1.8

0 -1.2000 1.0000 0.2000 -0.4000 0.2000 0 1.8

0 0.6000 0 -2.6000 0.2000 -0.6000 1.0000 0.6

0 -0.6000 0 2.6000 0.8000 1.6000 0 -0.6

here is the basic elements index

1 3 7

and here is the non-basics.....

5 2 6 4

the pivot element is the element

3 2

1.0000 0 0 4.6667 0.3333 1.0000 -1.3333 1

0 0 1.0 -5.0000 0 -1.0000 2.0000 3

0 1.0000 0 -4.3333 0.3333 -1.0000 1.6667 1

0 0 0 0 1.0000 1.0000 1.0000 0

here is the basic elements index

1 3 2

and here is the non-basics.....

5 7 6 4

the current soultion is optimal, the solution is not unique!.....

x = 1.0000 1.0000 3.0000 0 0 0

SECOND PAHSE II

A =

1.0 0 0 14/3 1

0 0 1.0000 -5.0000 3

0 1. 0 -13/3 1

0. 0 0 97/3 -7

the current soultion is optimal

x = 1 3 1 0

A =

5 -4 13 -2 1 1 0 20

1 -1 5 -1 1 0 1 8

-6 5 -18 3 -2 0 0 -28

the pivot element is the element

1 3

0.3846 -0.3077 1.0000 -0.1538 0.0769 0.0769 0 1.5385

-0.9231 0.5385 0 -0.2308 0.6154 -0.3846 1.00 0.3077

0.9231 -0.5385 0 0.2308 -0.6154 1.3846 0 -0.308

here is the basic elements index

3 7

and here is the non-basics.....

6 2 1 4 5

the pivot element is the element

2 2

-0.1429 0 1.0000 -0.2857 0.4286 -0.1429 0.5714 1.7143

-1.7143 1.0000 0 -0.4286 1.1429 -0.7143 1.8571 0.5714

0 0 0 0 0 1.0000 1.0000 0

here is the basic elements index

3 2

and here is the non-basics.....

6 7 1 4 5

the current soultion is optimal

the solution is not unique!.....

x = 0 0.5714 1.7143 0 0 0

7 R1+R3 -0.1429 0 1.0000 -0.2857 0.4286 1.7143

-6R2+R3 -1.7143 1.0000 0 -0.4286 1.1429 0.5714

1 6 -7 1 5 0

PhaseII

Now making the redaction elements of the basic

variables equal zero

-0.1429 0 1.0 -0.2857 0.4286 1.7143

-1.7143 1.0 0 -0.4286 1.1429 0.5714

10.2855 0 0 1.5717 1.1428 8.5717

solution is optimal

 

 

REVISED Method

First step using Phase I to find initial B.F.S then

you use the REVISED Method

But in both example the problem is solve from the first Phase.