Principles of Mathematics in Operations Research

Solutions 253

6'

1

}

4

i

i

~ 2

2

0

1

0

0

1

+ 2

4

0

0

5

0

+ 0

4 5 1 3 0 0

+ 0

1 5 0 2 5 0 1

+ 1

2

1

0

3

0

+ 1

1

0

0

2

1

convex combination of

extreme points

canonical combination of

extreme rays

1.

\xi

X\ 1

X3J0

-z|0

X 2 X 3

-1 0

-I 1

4 0

«1 «3

2 1

S 5

1 2

5 5

0 1

RHS1

2

1

-4

S_1(6-zl6)

2 1"

5 5

1 2

L 5 5 J

(

\

3

4

3

1

)-^2

1

7""

5

1

L

5

J

" 3"

5

6

I b J

The values of basic variables will change but not the optimal basis.

3. The solution above is
   problem!

,0,1) which satisfies the new constraint, no

8.3 a)

1. B = {si,52,33} -
   bounds and cjj =

> B = I,cB

(2,3,1,4).

6, J\f — {xi,X2,xs,X4} at their lower

xB =B~^1 b-B-lNx N

[30]

13

20

[1235]

1 100

0034

"1"

0

3

0

30

13

20

10

1

9

=

20

12

11

=

Sl

«2

S3

Z = Cg'xB + cJjXN = 2 • 0 + 3 + 0 = 5.

cN — CgB~ N — (2,3,1,4). Then, Bland's rule (lexicographical order)

marks the first variable. Since the reduced cost of #1 is positive and Xi is

at its lower bound; as x\ is increased, so is z. Hence, x± enters.