31
Subject to 2X1 + X2 + S1 = 600
X1 + X2 + S2 = 225
5X1 + 4X2 +S3 = 1000
X1 + 2X2 - S4 + R1 = 150
X1 , X2 , S1 , S2 , S3 , S4 , R1 >= 0
X1
X2
S4
S1
S2
S3
R1
B
Z
-3
-4
0
0
0
0
+M
S1
2
3
0
1
0
0
0
600
S2
1
1
0
0
1
0
0
225
S3
5
4
0
0
0
1
0
1000
R1
1
2
-1
0
0
0
1
150
Not in Canonical form because of +M entry on Z row for one basic variable (R1).
Pivot to replace +M on Z row by zero - Z row – M*R1 row:
X1
X2
S4
S1
S2
S3
R1
B
Z
(-3 –M)
(-4 -2M)
M
0
0
0
0
-150M
S1
2
3
0
1
0
0
0
600
S2
1
1
0
0
1
0
0
225
S3
5
4
0
0
0
1
0
1000
R1
1
2
-1
0
0
0
1
150
X1
X2
S4
S1
S2
S3
R1
B
Z
-1
0
-2
0
0
0
M
800
S1
½
0
3/2
1
0
0
-3/2
375
S2
½
0
½
0
1
0
-1/2
150
S3
3
0
2
0
0
1
-2
700
X2
1/2
1
½
0
0
0
½
75
 |