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: -669

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________________2006.

2006


1

2

3

4


 

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1.

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1.  . .

2.  . , , .

3.  . , , .

4.  . , . .. , , .


 

1

, , 1 1, 2 2, 3 3, . ( ) : 1 1, 2 2, 3 3.

. 1, 2 . . .

, , aij, , .

1=8, 2 = 15, 3 =12, 1 = 45, 2 = 7, 3 = 4, 1 = 20000, 2 = 30000, a11= 23,
a12 = 5, a13 = 1.4, a21 = 58, a22 = 10, a23 =3.8.

1. . (, ), xij, , .

:

:

:

2. ( ) :


:

bi

x11

x12

x13

x21

x22

x23

0 23 5 7/5 58 10 19/5

y1

8 1 0 0 1 0 0

y2

15 0 1 0 0 1 0

y3

12 0 0 1 0 0 1

y4

-20000 -45 -7 -4 0 0 0

y5

-30000 0 0 0 -45 -7 -4
bi

x11

x12

x13

x21

x22

x23

0 23 5 7/5 58 10 19/5
-150 0 -10 0 0 -10 0

y1

8 1 0 0 1 0 0
0 0 0 0 0 0 0

y2

15 0 1 0 0 1 0
15 0 1 0 0 1 0

y3

12 0 0 1 0 0 1
0 0 0 0 0 0 0

y4

-20000 -45 -7 -4 0 0 0
0 0 0 0 0 0 0

y5

-30000 0 0 0 -45 -7 -4
105 0 7 0 0 7 0

bi

x11

x12

x13

x21

y2

x23

-150 23 -5 7/5 58 -10 19/5
-228/5 0 0 -19/5 0 0 -19/5

y1

8 1 0 0 1 0 0
0 0 0 0 0 0 0

x22

15 0 1 0 0 1 0
0 0 0 0 0 0 0

y3

12 0 0 1 0 0 1
12 0 0 1 0 0 1

y4

-20000 -45 -7 -4 0 0 0
0 0 0 0 0 0 0

y5

-29895 0 7 0 -45 7 -4
48 0 0 4 0 0 4


bi

x11

x12

x13

x21

y2

y3

-978/5 23 -5 -12/5 58 -10 -19/5
464 -58 0 0 -58 0 0

y1

8 1 0 0 1 0 0
8 1 0 0 1 0 0

x22

15 0 1 0 0 1 0
0 0 0 0 0 0 0

x23

12 0 0 1 0 0 1
0 0 0 0 0 0 0

y4

-20000 -45 -7 -4 0 0 0
0 0 0 0 0 0 0

y5

-29847 0 7 4 -45 7 4
360 45 0 0 45 0 0

bi

x11

x12

x13

y1

y2

y3

1342/5 -35 -5 -12/5 -58 -10 -19/5

x21

8 1 0 0 1 0 0

x22

15 0 1 0 0 1 0

x23

12 0 0 1 0 0 1

y4

-20000 -45 -7 -4 0 0 0

y5

-29487 45 7 4 45 7 4

:


2

1

2

3

4

5

6

b1

b2

b3

a11

a12

a13

a14

1 2 3
8 2 6 2 2 2 0 2 6 1 = = = 1 2 1 0
.

a15

a16

a21

a22

a23

a24

a25

a26

a31

a32

a33

a34

a35

a36

.

 

8 0 0 2 1 1 1 2 0 1 1 0 0 1 0 max

 

1. :

( ) :


2. :

bi

x1

x2

2 -4 -6

x3

2 -1 2

x4

2 1 1

x5

1 1 -1

3. .

bi

x1

x2

2 -4 -6
6 -3 3

x3

2 -1 2
1 -0.5 0.5

x4

2 1 1
-1 0.5 -0.5

x5

1 1 -1
1 -0.5 0.5

bi

x1

x3

8 -7 3
21/4 21/4 -21/8

x2

1 -0.5 0.5
3/8 3/8 -3/16

x4

1 1.5 -0.5
3/4 3/4 -3/8

x5

2 0.5 0.5
-3/8 -3/8 3/16
bi

x4

x3

53/4 21/4 3/8

x2

11/8 3/8 5/16

x1

3/4 3/4 -3/8

x5

13/8 -3/8 11/16

.

: F=53/4, x1=3/4, x2=11/8, x3=0, x4=0, x5=13/8, x6=0.


3

.

1

2

3

b1

b2

b3

b4

b5

11

12

13

8 200 200 600 200 300 200 100 200 25 21 20
.

14

15

21

22

23

24

25

31

32

33

34

35

8 50 18 15 30 32 25 40 23 40 10 12 21

:

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200

A2

15 30 32 25 40 200

A3

23 40 10 12 21 600

bi

200 300 200 100 200 1000

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200
200

A2

15 30 32 25 40 600
300 200 100

A3

23 40 10 12 21 200
200

bi

200 300 200 100 200 600

L=5000+9000+6400+2500+4200=27300

r+m-1=7>5 .


1.

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200+e1
200 e1

A2

15 30 32 25 40 600
300 200 100

A3

23 40 10 12 21 200+e2
e2 200

bi

200 300+e1 200 100+e2 200 600+e1+e2

2.

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200+e1
0 200+e1

A2

15 30 32 25 40 600
200 100 200 100

A3

23 40 10 12 21 200+e2
e2 200

bi

200 300+e1 200 100+e2 200 600+e1+e2

3.

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200+e1
0 200+e1

A2

15 30 32 25 40 600
200 100 200-e2 100+e2

A3

23 40 10 12 21 200+e2
e2 200

bi

200 300+e1 200 100+e2 200 600+e1+e2

4.

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200+e1
0 e2+e1 200-e2

A2

15 30 32 25 40 600
200 300-e2 100+e2

A3

23 40 10 12 21 200+e2
e2 200

bi

200 300+e1 200 100+e2 200 600+e1+e2

5. 

6. 

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200+e1
0 e2+e1 200-e2

A2

15 30 32 25 40 600
200 300-e2 100+e2

A3

23 40 10 12 21 200+e2
200 e2

bi

200 300+e1 200 100+e2 200 600+e1+e2

B1

B2

B3

B4

B5

i

A1

25 21 20 50 18 200
0 200

A2

15 30 32 25 40 600
200 300 100

A3

23 40 10 12 21 200
200

bi

200 300 200 100 200 600


, .

: F=19100


4

b1

b2

c11

c12

c22

extr

a11

a12

a21

a22

p1

p2

.
1 2
8 1 2 1 0 1 max 1 2 1 1 16 8 £ =

:

:

, .

1. max min:

.

2. :

3. -:

:

, :

3 , x1=8-x2:

:

V1, V2, W :

:

4. :

, , :

, 1 2 , .

-:


bi

x2

u1

u2

V1

V2

-17M -4M -M 0 -M M
M M 0.5M -0.5M 0 -0.5M

z1

15 2 -1 1 1 0
1 1 0.5 -0.5 0 -0.5

z2

2 2 2 -1 0 -1
1 1 0.5 -0.5 0 -0.5
W 8 -1 0 0 0 0
0 0 0 0 0 0

bi

x2

z2

u2

V1

V2

-16M -3M 0.5M -0.5M -M 0.5M
3M 3M 1.5M -1.5M 0 -1.5M

z1

16 3 0.5 0.5 1 -0.5
-3 -3 -1.5 1.5 0 1.5

u1

1 1 0.5 -0.5 0 -0.5
1 1 0.5 -0.5 0 -0.5
W 8 -1 0 0 0 0
1 1 0.5 -0.5 0 -0.5

bi

u1

z2

u2

V1

V2

-13M 3M 2M -2M -M -M
13M -3M M 2M M M

z1

13 -3 1 2 1 1
13 -3 1 2 1 1

x2

1 1 0.5 -0.5 0 -0.5
0 0 0 0 0 0
W 9 1 0.5 -0.5 0 -0.5
0 0 0 0 0 0

bi

u1

z2

u2

z1

V2

0 0 3M 0 M 0

V1

13 -3 1 2 1 1

x2

1 1 0.5 -0.5 0 -0.5
W 9 1 0.5 -0.5 0 -0.5

u1=u2=z1=z2=V2=0

V1=13

x2=1

W=9

x1=8-x2=7

: x2=1, x1 =7,


1.  . ., . . . : . ., 2000. 436.

2.  .. 1. .

3.  ..

-

 

 

 

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