Engineering Optimization: Theory and Practice, Fourth Edition

Table 4.1

Original System of Equations

Admissible (original) variable

Artificial variable

Objective variable

x

1

x^2

· · ·

xj

· · ·

xn

xn

+

1

xn

+

2

· · ·

xn

+

m

−

f

−

w

Constant

←−−−−−−

Initial basis

−−−−−−→

a

11

a^12

a

1 j

a^1

n

1

b

1

a

21

a^22

a

2 j

a^2

n

1

b

2

 

A

1

 

A

2

 

A

j

 

A

n

...

...

...

...

a

m^1

am

2

a

mj

amn

1

b

m

c^1

c^2

cj

cn

0

0

0

1

0

0

d

1

d^2

dj

d

n

0

0

0

0

1

−

w

0

183