1. (.1).
cj | -c0 | ck+1 | cj* | cn | c0 | |||
ci | ai0 | xk+1 | xj* | xn | ||||
c1 | x1 | a10 | a1+1 | a1j* | a1n | |||
c2 | x2 | a20 | a2+1 | a2j* | a2n | |||
ci* | xi* | ai*0 | ai*k+1 | ai*j* | ai*n | |||
ck | xk | ak0 | akk+1 | akj* | akn | |||
∆j | z=∆0 | ∆k+1 | ∆j* | ∆n | - |
2. , . . , .
3. :
.
4. : , . , 13, , 5.
5. ( ). , .
6. 7. , .
7. , , .
8. . , .
9. .
10. :
) , :
;
) , , :
;
) , , :
;
) , , :
.
. , , . . .
, , , , .
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:
j1 | j* | |||
i1 | ||||
i* |
j* | j2 | |||
i* | ||||
i2 |
j* | j2 | |||
i1 | ||||
i* |
j1 | j* | |||
i* | ||||
i2 |
11. , .
, .
12. 4.
13. .
. : , . 6000 , 20000 - 10000 - . :
1 , .-. | 1 , | ||
2,5 | |||
2,5 | 1,5 |
. - . .
:
1 - , ;
2 - , ;
3 - , .
z - .
:
. :
, 1000 .
1 | cj | 0 | 175 | 125 | 140 | c0 |
ci | aj0 | x1 | x2 | x3 | ||
0 | x4 | 6 | 1 | 1 | 1 | 6:1=6 |
0 | x5 | 20 | 5 | 2,5 | 2,5 | 20:5=4 i* |
0 | x6 | 10 | 2 | 1 | 1,5 | 10:2=5 |
∆j | 0 | -175 | -125 | -140 | - |
j*
2 | cj | 0 | 0 | 125 | 140 | c0 |
ci | aj0 | x5 | x2 | x3 | ||
0 | x4 | 2 | -1/5 | 1/2 | 1/2 | 2:1/2=4 i* |
175 | x1 | 4 | 1/5 | 1/2 | 1/2 | 4:1/2=8 |
0 | x6 | 2 | -2/5 | 0 | 1/2 | 2:1/2=4 |
∆j | 700 | 35 | -37,5 | -52,5 | - |
j*
3 | cj | 0 | 0 | 125 | 0 | c0 |
ci | aj0 | x5 | x2 | x4 | ||
140 | x3 | 4 | -2/5 | 1 | 2 | |
175 | x1 | 2 | 2/5 | 0 | -1 | |
0 | x6 | 0 | -1/5 | -1/2 | -1 | |
∆j | 910 | 14 | 15 | 105 | - |
, .
, 1000 :
(2000; 0; 4000; 0; 0; 0); max z =910000.
1 = 2000 - ;
2 = 0 - ;
3 = 4000 - .
, x4= x5= x6=0, 910000 .
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1.6.
.
2.1.1. ( Reddy Mikks.) Reddy Mikks : (1) (2) . . . 6 8 . 1 .
, 1 2 1. , , 1 2 .
: 3 . . 2, 2 . . 1.
( ) | , | ||
1 | 2 | ||
, ?
.
:
1. ? , ( ) ?
2. , , ?
3. , , () ?
, . , .
( ) , ( ) , .
. .
. ,
1 1 ( );
2 2 ( ).
. 1 2 3 . ., 3 2 . . 1 1 2 . . . 2 1.
, ( . .) z, : () 2 1 z=3 2 - 2∙x1.
. .
(. ):
2 |
:
- ( 1 2),
- ( 1).
(. . ) , (. . ). , , . , :
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- ( 1),
- ( 2).
, .
(1 2) 1 2 ( ),
- ( )
? , ( ) . .
1. , (.. 2 1) () . , , , 2 2,5 . . 2 , , , , 2 , 3 . . 3 . . 2,5 . . . . . 2 .
2. , . , . , , , , .
2.1.1. .
() .
1) 1 2 1 .
[: 1-2≥ 1].
2) 6 , 3 . [: ].
3) 1 2.
[O: 1-2≥ 0].
() , .
1) 2 =1, 1 =4; 2) 2 =2, x1 =2; 3) 2 = , 1 = ; 4) 2 =2, 1 =1; 5) 2 =2, 1 =-1.
[: 1) 5) , ].
() 2 =2, x1 =2. .
1) ( ) . [: 0].
2) . [: 2].
() , . () .
[: 2) z =10; 3) z =122/3; 4) z =8, . . ].
() ?
[. , , . (), . .]
1.7.
Reddy Mikks. , . , . , (. . 3).
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, . . () , . () . 1.1.
. 1.1.
2 ≥0 1 ≥0 ( , 2 1). 2, 1 , ≤ = . , , , . ABCDEF . 1.1.
, ABCDEF, , , , . , , , , , z=3 2 - 2∙x1. . 1.2 , . , z, , (. . ). . 1.2 : z =6 z =9. (!)
, , , , . . 1.2 , . (1) (2) (. . 1.1), 2 1 :
: 2 =31/3, 1 = 11/3. , 2 31/3 , 1 - 11/3 . , , . .
. 1.2.
: z=3 2 - 2∙x1 .
: 1 = 11/3 ., 2 =31/3 ., . .
2.1.2.
() Reddy Mikks, , , , . ( . 1.1.).
1) 1 3 .
[. ABCGF, - ].
2) 1 2 .
[. EDG, D, 2 = 1 =2 z =10].
3) 1 1 2.
[. EF, , 2 =1, x1 =2, z =7].
4) 8 .
[. BCJ, J, 2 =6, 1 =0 z = 18].
5) 8 , 1 2 1 .
[. ].
() . 1.2, :
1) z=3x2+1. [: 2 =4, 1 = 0, - ].
2) z=3x2+1,51. [. , ].
3) z z=x2+31. [: x2 =2, 1= 2, - D ].
4) . 2 . ?
[. 12. , ].
, 2.1.2(6), : ( ) ( . 1.2 , , , D, F). , , (. . ). , . 2, , , .
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