:

:

, , - . :

1.   -

2.  

3.  

>=, (-1) <=.

³ . . .

:

F = 51 +62 max

-10x1 - 6x2 ³-60

-4x1 + 9x2 £ 36

4x1 - 2x2 £ 8

x1,x2³0 x1,x2-

:

F = 51 +62 max

10x1 + 6x2 + 3 =60

-4x1 + 9x2 +4= 36

4x1 - 2x2 +5 = 8

x1,x2,x3,x4,x5 ³0 x1,x2-

. .

, -.

0

1

2

3

4

5

1

3

0 60 10

: 96

1 0 0
2

4

0 36 -4 9 0 1 0
3

5

0 8 4 -2 0 0 1
4 F 0 -5 -6 0 0 0

1 -


- :

1.   -

- . .

. x1 1 ..

0 . - . - , 䒺 . . 1 2. , , 0 1.

1, 2 , = 0

=(0;0;60;36;8)

2.   , ( 4) , -.

(-5) (-6), .

3.   . , . 2 |-6|>|-5|

4.   . , . ( )

Min = ( 60/6; 36/9) = 4 2.

5.   - .

aij=aij- (k* nj)/ank k- , n-

aij - , - j

aij - , -j -

k-- . -.

nj-- -.

ank -.

a10= 60 (36*6)/9 = 36

a11= 10 +(6*4)/9 = 38/3

0

: 38/31

2

3

4

5

1

3

0 36 0 0 -1 1/5

0

2

2

6 4 -4/9 1 1 1/5 0
3

5

0 16 28/9 0 0 3/5 1
4 F 24

-23/3

0 0 1 1/5 0

2

1=(0;4;36;0;16) F(X1) = 24

. 1

Min = ( 36/38*3;16/4;9) = 54/19 3

 

3

0

1

2

3

4

5

1

1

5 54/19 1 0 3/38 -1/19 0
2

2

6 100/19 0 1 2/57 5/57 0
3

5

0 136/19 0 0 -14/57 22/57 1
4 F 870/19 0 0 21/38 5/19 0

X3= ( 54/19;100/19;0;0;136/19) F3(X3) = 45 15/19

, . , .

2.

1=54/19, 2=100/19

: F(a*ij)*xij>= F(b*ij), a*ij b*ij .

ϳ , . , , .

F(x1)>F(x2) (16/19 >5/19)

-3/383-18/194 + 6 = -16/19

4

0

1

2

3

4

5

6

1

1

5 54/19 1 0 3/38 -1/19 0 0
2

2

6 100/19 0 1 2/57 5/57 0 0
3

5

0 136/19 0 0 -14/57 22/19 1 0
4

6

0 -16/19 0 0 -3/38

-18/19

0

1

5 F 870/19 0 0 23/38 5/19 0 0

4 = ( 54/19;100/19;0;0;135/19;-16/19) F(X4) = 45 15/19

..

. .

3.

³ - :

1.  

4 = ( 54/19;100/19;0;0;135/19;-16/19) F(X4) = 45 15/19

2.   .

, .

3.   . ,

4

4.   . , . ( )

Min = (23/38*38/3;5/19*19/18) = 5/18 4

5

0

1

2

3

4

5

6

1

1

5 26/9 1 0 1/12 0 0 -1/18
2

2

6 140/27 0 1 1/36 0 0 5/54
3

5

0 1048/171 0 0 -13/38 0 1 11/9
4

4

0 8/9 0 0 1/12 1 0 -19/18
5 F 410/9 0 0 7/12 0 0 5/18

5= (26/9;140/27;0;0;8/9;1048/171) F5 = 45 5/9

F(x1) = f ( 2 8/9) = 8/9

F (x2) = f ( 5 5/27) = 5/27

-1/123 17/186 + 7 = -8/9

6

0

1

2

3

4

5

6

7

1

1

5 26/9 1 0 1/12 0 0 -1/18 0
2

2

6 140/27 0 1 1/36 0 0 5/54 0
3

5

0 1048/171 0 0 -13/38 0 1 11/9 0
4

4

0 8/9 0 0 1/12 1 0 -19/18 0
5

7

0 -8/9 0 0 -1/12 0 0

-17/18

1

6 F 410/9 0 0 7/12 0 0

5/18

0

7

0

1

2

3

4

5

6

7

1

1

5 50/17 1 0 3/34 0 0 0 -1/17
2

2

6 260/51 0 1 1/57 0 0 0 5/57
3

5

0 1608/323 0 0 -436/969 0 1 0 11/17
4

4

0 32/17 0 0 3/17 1 0 0 -19/17
5

6

0 16/17 0 0 3/34 0 0 1 -18/17
6 F 770/17 0 0 19/34 0 0 0 5/17

6= ( 50/17;260/51;0;32/17;1608/323;16/17) F6 = 45 5/17

:

F(x1) = f(2 16/17) = f(16/17) = 16/17

F(x2) = f (5 5/51) = f(5/51) = 5/51

F(x1)> F(x2)

-3/34x3 16/17x7 + x8 = -16/17

8

0

1

2

3

4

5

6

7

8

1

1

5 50/17 1 0 3/34 0 0 0 -1/17 0
2

2

6 260/51 0 1 1/57 0 0 0 5/57 0
3

5

0 1608/323 0 0 -436/969 0 1 0 22/17 0
4

4

0 32/17 0 0 3/17 1 0 0 -19/17 0
5

6

6 16/17 0 0 3/34 0 0 1 -18/17 0
6

8

0 -16/17 0 0 -3/34 0 0 0

-16/17

1
7 F 770/17 0 0 19/34 0 0 0 5/17 0

9

0

1

2

3

4

5

6

7

8

1

1

5 3 1 0 3/32 0 0 0 0 0
2

2

6 5 0 1 1/96 0 0 0 0 0
3

5

0 70/19 0 0 -521/912 0 1 0 0 0
4

4

0 3 0 0 9/32 1 0 0 0 0
5

6

0 2 0 0 3/16 0 0 1 0 0
6

7

0 1 0 0 3/32 0 0 0 1 1
7 F 45 0 0 17/32 0 0 0 0 0

*=(3; 5) F*=45

4. .

.

1)   , =.

10x1 + 6x2 =60 (1)

-4x1 + 9x2 = 36 (2)

4x1 - 2x2 = 8 (3)

x1=0, (4)

x2=0 (5)

x1 = 0 , x2 =0 .

. , , , .

2)   .

, .. x1,x2³0 x1,x2-

. -. , .

3)   -.


10



4


(2)

6

-9

(3)

(1)

-4


10


 


4

( I )

-38/3

 


(2)

6

-9

(3)

(1)

-4

, , (I) (1) . .


-31 + 92 = 38 1=26/9

. (26/9; 140/27)

101+ 62 = 60 2=140/27 F ( B) = 45 5/9

-1/123 17/186 = -8/9 .

-1/123*(60 101- 62) 17/18*(38 + 31 92) = -8/9

-21 + 92 = 40 2- .

7= 40 + 21 - 92


10


 

4

-38/3

 
( II ) (I)

(2)

6

-9

2 16/17

-20 (II) (3)

(1)

-4


10


 

D

4

(III)

( II ) (I)

(2)

6

-9

2 16/17

-20 (II) (3)

(1)

-4

:

-3/343 16/177 = -16/17

7 2

-3/34 * ( 60 101 62) 16/17*(40 + 21 92) = -16/17

-1 + 92 = 42 .

. D (1) (III)

101 + 62 = 60

-1 + 92 = 42

1=3; 2=5. F(D)=45

.D (3;5)

:

-. . , . .. ,.. , . .

:

1.   .. :(

2.   : ( .. : Ҳ,1998-20)


 
2012 , , .