Ch44.2 The graphical method of GP
4.3 Simplex Method
1978(H.A.Simon--,1916)“”“”“”“”“”

LP
4
4.1
4.1.1
4.1.1
40x1+30x2+50x3-d1+ =3200
40x1+30x2+50x3=3200
4.1.1
4.1.1
4.1.1
4.1.1
4d4 d4+A, d5d5+B d4+ d5+ d4+ + d5+
4
Pjj=1,2,3,4P1P2…

4.1.1
“min”, “-”
4
2di- di+d-×d=0
3
4.1.2
4
:
4.1.2
4
4
4
4
4.1.2
4

4

4
1
2
3
4
5
()
12
10
15
13
20
rij
1
4.32
5
5.84
5.2
6.56
2
3.52
3.04
5.08
4.2
6.24

3.16
2.2
3.56
3.28
4.08

2.24
3.12
2.6
2.2
3.24
()
3.31
3.34
4.27
3.72
5.03
1
2
4
4520% ,
4
WinQSB4-8
x1
x2
x3
x4
x5

1
2

4
1
3800540

4
4
4
4.2
4
4.2
4-4


A
A(20,40)
D(80/9,560/9)
D d2-=0, 2d3=2×200/9=400/9
4-52
3P1…PiPi+1P1…Pi
4.3
4
4-6
4.3
4
[ ]
4-6P1P2x1-P2<0x1d1+d2-4-7
[ ]
-2/3P2<0d1+x14-8
4-7d2+P1-2/3P2“”P1P2“”-3P2+5P32P2-4P4
4.3
Cj
0
0
P1
0
0
P1
P2
0
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
0
x2
1
2/3
-2/3
1/3
20
0
x1
1
[1/3]
2/3
10
P2
d3-
2/3
2/3
1
-1
20
Cj-Zj
P1
1
1
P2
2/3
-2/3
2/3
-2/3
1
X040
Cj→
0
0
P1
0
0
P1
P2
0
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
0
x2
2
1
1
-1
40
0
d1+
3
-1
1
2
-2
30
P2
d3-
-2
-2
2
1
-1
0
Cj-Zj
P1
1
1
P2
2
2
-2
1
4.3
4
Cj
0
0
P1
0
0
P1
P2
P2
0
P3
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
P1
d1-
[10]
5
1
-1
400→
0
d2-
7
8
1
-1
560
P2
d3-
2
2
1
-1
120
0
d4-
1
2.5
1
-1
100
Cj-Zj
P1
-10
-5
1
1
P2
-2
-2
2
P3
1
Cj
0
0
P1
0
0
P1
P2
P2
0
P3
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
0
x1
1
1/2
1/10
-1/10
40
0
d2-
9/2
-7/10
7/10
1
-1
280
P2
d3-
1
-1/5
1/5
1
-1
40
0
d4-
[2]
-1/10
1/10
1
-1
60→
Cj-Zj
P1
1
1
P2
-1↑
1/5
-1/5
2
P3
1
Cj
0
0
P1
0
0
P1
P2
P2
0
P3
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
0
x1
1
5/40
-5/40
-1/4
1/4
25
0
d2-
-19/40
19/40
1
-1
-9/4
9/4
145
P2
d3-
-3/20
[3/20]
1
-1
-1/2
1/2
10→
0
x2
1
-1/20
1/20
1/2
-1/2
30
Cj-Zj
P1
1
P2
3/20
-3/20↑
2
1/2
-1/2
P3
1
Cj
0
0
P1
0
0
P1
P2
P2
0
P3
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
0
x1
1
5/6
-5/6
-2/3
2/3
100/3
0
d2-
1
-1
-19/6
19/6
-2/3
2/3
340/3
0
d1+
-1
1
20/3
-20/3
-10/3
10/3
200/3→
0
x2
1
-1/3
1/3
[2/3]
-2/3
80/3
Cj-Zj
P1
1
P2
1
1
P3
1
Cj
0
0
P1
0
0
P1
P2
P2
0
P3
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
0
x1
1
1
1/2
-1/2
60
0
d2-
1
1
-1
-7/2
7/2
140
0
d1+
5
-1
1
5
-5
200
0
d4-
3/2
-1/2
1/2
1
-3/4
40
Cj-Zj
P1
1
P2
1
1
P3
1
Z=108.88
Cj
0
0
P1
P1
P3
0
0
P2
0
P4
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
0
x1
1
1/8
-1/8
-1/4
1/4
25
P3
d2-
-19/40
19/40
1
-1
-9/4
9/4
145
0
d3-
-3/20
3/20
1
-1
-1/2
[1/2]
10
0
x2
1
-1/20
1/20
1/2
-1/2
30
Cj-Zj
P1
1
1
P2
1
P3
19/40
-19/40
1
9/4
-9/4
P4
1
4-17
4-15
Cj
0
0
P1
P1
P3
0
0
P2
0
P4
b
CB

x1
x2
d1-
d1+
d2-
d2+
d3-
d3+
d4-
d4+
0
x1
1
1/5
-1/5
-1/2
1/2
20
P3
d2-
1/5
-1/5
1
-1
-9/2
9/2
100
P4
d4+
-3/10
3/10
2
-2
-1
1
20
0
x2
1
-1/5
1/5
1
-1
40
Cj-Zj
P1
1
1
P2
1
P3
-1/5
1/5
1
9/2
-9/2
P4
3/10
-3/10
4