1. Max f(x) = 4x1 + 3x2 Max f(x) = 4x1 + 3x2
sujeta a 2x1 + 3x2 ≤ 6 sujeta a 2x1 + 3x2 + h1 = 6
-3x1 + 2x2 ≤ 3 -3x1 + 2x2 + h2 = 3
2x2 ≤ 5 2x2 + h3 = 5
2x1 + x2 ≤ 4 2x1 + x2 + h4 = 4
x1, x2 ≥ 0 x1, x2, h1, h2, h3, h4 ≥ 0
Base f(x) x1 x2 h1 h2 h3
f(x) 1 -4 -3 0 0 0
h1 0 2 3 1 0 0
h2 0 -3 2 0 1 0
h3 0 0 2 0 0 1
h4 0 2 1 0 0 0
Base f(x) x1 x2 h1 h2 h3
f(x) 1 0 -1 0 0 0
h1 0 0 2 1 0 0
h2 0 0 3 1/ 2 0 1 0
h3 0 0 2 0 0 1
x1 0 1 1/ 2 0 0 0
Base f(x) x1 x2 h1 h2 h3
f(x) 1 0 0 1/ 2 0 0
x2 0 0 1 1/ 2 0 0
h2 0 0 0 -1 3/ 4 1 0
h3 0 0 0 -1 0 1
x1 0 1 0 - 1/ 4 0 0
Solución óptima Var. Coef. E
f(x) = 9 x1 4
x1 = 1 1/ 2 x2 3
x2 = 1
Max f(x) = 4x1 + 3x2
sujeta a 2x1 + 3x2 ≤ 6
-3x1 + 2x2 ≤ 3 f(x) = 9
2x2 ≤ 5

2. 2x1 + x2 ≤ 4
x1, x2 ≥ 0

3. f(x) - 4x1 - 3x2 = 0
h2, h3, h4 ≥ 0
h4 Soluci.
0 0
0 6 3
0 3 -1
0 5 #DIV/0!
1 4 2
h4 Soluci.
2 8
-1 2 1
1 1/ 2 9 2 4/ 7
0 5 2 1/ 2
1/ 2 2 4
h4 Soluci.
1 1/ 2 9
- 1/ 2 1
3 1/ 4 5 1/ 2
1 3
3/ 4 1 1/ 2
valor Coef. Tecnolog. L.I. L.D
1 1/ 2 2 3 6 6
1 -3 2 -2 1/ 2 3
0 2 2 5
2 1 4 4
x1 x2

5. Max U = 55m + 25s Max U = 55m + 25s
sujeta a 1m + 1s ≤ 60 sujeta a 1m + 1s + h1= 60
3m + 1s ≤ 115 3m + 1s +h2 =115
6m + 25s ≤ 297.5 6m + 25s +h3=297.5
19m + 11s ≤ 510 19m + 11s +h4= 510
m, s ≥ 0 m, s ≥ 0
Base f(x) x1 x2 h1 h2
f(x) 1 -55 -25 0 0
h1 0 1 1 1 0
h2 0 3 1 0 1
h3 0 6 25 0 0
h4 0 19 11 0 0
Base f(x) x1 x2 h1 h2
f(x) 1 0 6 16/19 0 0
h1 0 0 8/19 1 0
h2 0 0 - 14/19 0 1
h3 0 0 21 10/19 0 0
x1 0 1 11/19 0 0
Base f(x) x1 x2 h1 h2
f(x) 1 0 0 -16 1/ 4 0
x2 0 0 1 2 3/ 8 0
h2 0 0 0 1 3/ 4 1
h3 0 0 0 -51 1/ 8 0
x1 0 1 0 -1 3/ 8 0
Solución óptima Var.
U= 937 1/ 2 m
m= -18 3/ 4 s
s= 78 3/ 4
Max U = 55m + 25s

6. sujeta a 1m + 1s ≤ 60
3m + 1s ≤ 115 f(x) =
6m + 25s ≤ 297.5
19m + 11s ≤ 510
m, s ≥ 0

7. U -55m - 25s = 0
+ h1= 60
+h2 =115
1s +h4= 510
h3 h4 Soluci.
0 0 0
0 0 60 60
0 0 115 38 1/ 3
1 0 297 1/ 2 49 4/7
0 1 510 26 16/19
h3 h4 Soluci.
0 2 17/19 1476 6/19
0 - 1/19 33 3/19 78 3/ 4
0 - 3/19 34 9/19 -46 11/14
1 - 6/19 136 17/38 6 21/62
0 1/19 26 16/19 46 4/11
h3 h4 Soluci.
0 3 3/ 4 937 1/ 2
0 - 1/ 8 78 3/ 4
0 - 1/ 4 92 1/ 2
1 2 3/ 8 -1558 3/ 4
0 1/ 8 -18 3/ 4
Coef. E valor Coef. Tecnolog. L.I.
55 1 1 1 2
25 1 3 1 4
6 25 31
19 11 30

8. m s
80

9. L.D
6
3
5
4