- .
:
L=Cծmax (1)
: £ (2)
³ 0 (3)
:
Z=BY→min (4)
: Y³ (5)
Y ³ 0 (6)
, . (2) ( ) m xn+1,,xn+i,,xn+m, (5) () - n ym+1,,ym+j,, yn+m, i(j) , .
- :
(7)
(8)
c (7), (8) m+n . (7) xn+1,,xn+i,,xn+m, (8) ym+1,,ym+j,, yn+m.
(9)
(10)
. xn+1 (9), a11, a12,,a1n:
.
(10) y1:
xn+1 y1. .
I | |
x1 x2 xj . xn ↕ ↕ ↕ ↕ ym+1 ym+2 ym+j . ym+n | xn+1 xn+2 xn+i . xn+m ↕ ↕ ↕ ↕ (11) y1 y2 yj . ym |
II |
, , xn+j (j=1,2,,m) (9), , yj ( xn+j) (10).
. () - , .. i=1,2,,m j=1,2,,n :
x*j>0, y*m+j=0; x*n+i>0, y*j=0, , y*j>0, x*n+i=0; y*m+j>0, x*j=0.
. (7) I II,
(12)
(13)
(12) yj ³ 0 :
(14)
, (13) xj ³ 0 , :
(15)
(14) (15) , x*j, x*n+i, y*i, y*m+j.
L(*)= Z(Y*) , (14) (15) , .
|
|
, (14) (15)
, .
, :
:
, x*n+i>0, y*j=0, , y*j>0, x*n+i=0 ( ); x*j>0, y*m+j=0 , y*m+j>0, x*j=0.¨
: (11) - , .. , , , , , , .