, .
:
2 . 1 2. 4 1-4. S1=19, S2=13, S3=15, S4=18. 1 1, 2, 4. 1 2 .
1=7 , 2=5 .
1 2 1 2.
1 2 | ||
1 | 2 3 | |
2 | 2 1 | |
3 | - 3 | |
4 | 3 - |
21+32<=19
21+12<=13 (1)
3x2<=15
3x1<=18
X1=>0, x2=>0 (2)
R(x1,x2)=7x1+5x2->max (3)
(1-3) 1*, 2*, (2) (3).
2) (1-3) .
(1-3).
R(x1,x2)=7x1+5x2->max
21+32=19
21+12=13
3x2=15
3x1=18
X1=0
.
60.
4,
21+32=19
21+2=13
1=5
2=3
.
R(x*)=R(x1,x2)=7*5+5*3=50->max
1* 2*
2*5+3*3=19
2*5+1*3=13
3*3=9<15
, 6 3 .
.
, , .
A11x1+a12x2+a1mxn=b1
A21x1+a22x2+a2mxn=b2
An1x1+an2x2+anmxn=bn
.
m- 1 (). . m-n .
n m.
|
|
.
X1-x2-2x3+x4=0
2x1+x2+2x3-x4=2
N=4
M=2
.
, .
:
3 .
1 2
3 4 , .
1 2 .
31=2, 1=2/3
. 3,4.
1 0, . . n-m- 0. , .
:
X1-x2-2x3+x4=0
2x1+x2+2x3-x4=2
1 2 , 3 4 . 3 =0 4=0. 1-x2=0
, . .
, .
:
1) ( )
2)
3) ( )
4) ( )
. , , .