Minimizar z(x) = 4 x1 + x2 Sujeto a 3 x1 + x2 = 3 4 x1 + 3

Minimizar z(x) = 4 x1
Sujeto a
3 x1
4 x1
x1
x1
+
x2
+
x2
+ 3 x2
+ 2 x2
x2
=
≥
≤
≥
3
6
4
0
Forma standard
Minimizar z(x) = 4 x1
Sujeto a
3 x1
4 x1
x1
x1
+
x2
+
x2 +
a1
+ 3 x 2 – s2 +
+ 2 x2 +
s3
x2
s2
s3 a 1
a2
a2
=
=
=
≥
3
6
4
0
=
=
=
≥
3
6
4
0
Fase I
a1 + a 2
Minimizar w(a) =
Sujeto a
3 x1 +
x2 +
a1
4 x 1 + 3 x 2 – s2 +
x 1 + 2 x2 +
s3
x2
s2
s3 a 1
x1
a2
a2
Método Simplex Fase I
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
F13
F14
a1
a2
s3
-w
-w′
-w′′
x1
3
4
1
0
-3
-7
x2
1
3
2
0
-1
-4
s2
0
-1
0
0
0
1
s3
0
0
1
0
0
0
a1
1
0
0
1
0
0
a2
0
1
0
1
1
0
b
3
6
4
0
-3
-9
x1
a2
s3
-w
x1
1
0
0
0
x2
1/3
5/3
5/3
-5/3
s2
0
-1
0
1
s3
0
0
1
0
a1
1/3
-4/3
-1/3
7/3
a2
0
1
0
0
b
1
2
3
-2
x1
x2
s3
-w
x1
1
0
0
0
x2
0
1
0
0
s2
1/5
-3/5
1
0
s3
0
0
1
0
a1
3/5
-4/5
1
1
a2
-1/5
3/5
-1
1
b
3/5
6/5
1
0
F4-F1
F5-F2
F1/3
F2-4F7
F3-F7
F6+7F7
F7-F12/3
F8/(5/3)
F9-(5/3)F12
F10+(5/3)F12
Método Simplex Fase II
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
x1
x2
s3
-z
-z′
-z′′
x1
1
0
0
4
0
0
x2
0
1
0
1
1
0
s2
1/5
-3/5
1
0
-4/5
-1/5
s3
0
0
1
0
0
0
b
3/5
6/5
1
0
-12/5
-18/5
x1
x2
s2
-z
x1
1
0
0
0
x2
0
1
0
0
s2
0
0
1
0
s3
-1/5
3/5
1
1/5
b
2/5
9/5
1
-17/5
Solución óptima:
x1 = 2/5
x2 = 9/5
s2 = 1
z* = 17/5
F4-4F1
F5-F2
F1-F9/5
F2+(3/5)F9
F6+F9/5