( , ..).
n m .
Si (i=1,2,...,m) - ;
bi - i- ;
Pj (j=1,2,....n) - ;
aij - i- , j- ;
Cj - , j- . (. . 1.).
i- , j- | |||||
P1 | P2 | ... | Pn | ||
S1 | b1 | a11 | a12 | ... | a1n |
S2 | b2 | a21 | a22 | ... | a2n |
... | ... | ... | ... | ... | |
Sm | bm | am1 | am2 | ... | amn |
. | C1 | C2 | ... | Cn |
, .
xj - j- , .
: L=C1x1+C2x2+×××+Cnxn (1) :
(2)
xj ³ 0, (j=1,2,×××,n), bi ³ 0 (i=1,2, ×××,m). (3)
aij , m n , i- , j- , A; bi B=(b1,b2,...,bm) ( ). X=(x1,x2,...,xn), , P1,P2,...,Pn . C=(C1,C2,...,Cn).
, , , . , . , S1,S2,...,Sm . . .
.
m bi (I=1,2,,m) . n - dj (j=1,2,,n) . aij i- , j- , j , j- . , .
xj (j =1,2,,n) j- , , , :
|
|
L= : , i=1,2,,m, 0£xj£dj, j=1,2,,n.
1. P1, P2 4 () S1, S2, S3, S4. , , , , , 2.
, .
2.
P1 | P2 | ||
S1 | |||
S2 | |||
S3 S4 | - | - | |
. |
. - .
x1 P1, x2 - P2, :
x1 ³ 0, x2 ³ 0 (4)
, , , . P1 ,
x1 = 0, x1 > 0. P2, x2 = 0 x2 > 0. , x1 x2 : x1 ³ 0, x2 ³ 0.
- , x1 x2: L=2x1 + 3x2 () (5).
, : (5) (4).