problema de examen de sistema de operaciones

1. Instituto Tecnológico Nacional
De México
Campus Tláhuac II
Investigación de Operaciones
Tema: Ejercicio , método simplex
Profesor: Ariel Tenorio Núñez
Alumno: Cisneros Flores Ramses
191110148
191110148@ittlahuac.edu.mx
ILOG
5 A

2. MODELO 5 CFE
Desde San Juan Tecomitl Tetelco Mixquic
P1 8 6 10 9 ≤35
P2 9 12 13 7 ≤50
P3 14 9 16 5 ≤40
≥45 ≥20 ≥30 ≥30
Paso 2
𝑍𝑚𝑖𝑛 = 8𝑥11 + 6𝑥12 + 10𝑥13 + 9𝑥14 + 9𝑥21 + 12𝑥22 + 13𝑥23 + 7𝑥24 + 14𝑥31 + 9𝑥32 + 16𝑥33 + 5𝑥34
Restricciones (Oferta)
𝑍𝑚𝑖𝑛 = 8𝑥11 + 6𝑥12 + 10𝑥13 + 9𝑥14 ≤ 35 ℎ1
9𝑥21 + 12𝑥22 + 13𝑥23 + 7𝑥24 ≤ 50 ℎ2
14𝑥31 + 9𝑥32 + 16𝑥33 + 5𝑥34 ≤ 40 ℎ3
Restricciones (Demanda)
8𝑥11 + 9𝑥21 + 14𝑥31 ≥ 45 𝑒1
6𝑥12 + 12𝑥22 + 9𝑥23 + 7𝑥24 ≥ 20 𝑒2
10𝑥13 + 13𝑥23 + 16𝑥33 ≥ 30 𝑒3
9𝑥14 + 7𝑥24 + 5𝑥34 ≥ 30 𝑒4
𝑥1, 𝑥2, 𝑥3 ≥ 0

3. VB z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 -8 -6 -10 -9 -9 -12 -13 -7 -14 -9 -16 -5 0 0 0 0 0 0 0 0 /-16
H1 0 8 6 10 9 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 35 /0
H2 0 9 12 13 7 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 50 /0
H3 0 14 9 16 5 0 0 0 0 0 0 16 0 0 0 1 0 0 0 0 40 /16
E1 0 8 0 0 0 9 0 0 0 14 0 0 0 0 0 0 -1 0 0 0 41 /0
E2 0 0 6 0 0 0 12 0 0 0 9 0 0 0 0 0 0 -1 0 0 20 /0
E3 0 0 0 10 0 0 0 13 0 0 0 16 0 0 0 0 0 0 -1 0 30 /16
E4 0 0 0 0 9 0 0 0 7 0 0 0 5 0 0 0 0 0 0 -1 30 /0
VB z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 -8 -6 0 -9 -9 -12 0 -7 -14 -9 0 -5 0 0 0 0 0 -1 0 30 /-14
H1 0 8 6 10 9 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 35 /0
H2 0 0 0 0 0 9 12 13 7 0 0 0 0 0 1 0 0 0 0 0 50 /0
H3 0 0 0 -10 0 0 0 -13 0 14 9 0 5 0 0 1 0 0 0 0 10 /14
E1 0 8 0 0 0 9 0 0 0 14 0 0 0 0 0 0 -1 0 0 0 45 /14
E2 0 0 6 0 0 0 12 0 0 0 9 0 0 0 0 0 0 -1 0 0 20 /0
X33 0 0 0 5/8 0 0 0 13/16 0 0 0 1 0 0 0 0 0 0 -
1/16
0 15/8 /0
E4 0 0 0 0 9 0 0 0 7 0 0 0 5 0 0 0 0 0 0 -1 30 /0
𝑍 − 8𝑥11 + 6𝑥12 − 10𝑥13 − 9𝑥14 − 9𝑥21 − 12𝑥22 − 13𝑥23 − 7𝑥24 − 14𝑥31 − 9𝑥32 − 16𝑥33 − 5𝑥34 = 03𝑥1 + 𝑥2 + 𝑥3 + ℎ1
= 60𝑥1 − 𝑥2 + 2𝑥3 + ℎ2 = 10𝑥1 + 𝑥2 − 𝑥3 − ℎ3 = 20𝑥1, 𝑥2,𝑥3 ≥ 0
8𝑥11 + 6𝑥12 + 10𝑥13 + 9𝑥14 + ℎ1 = 35
9𝑥21 + 12𝑥22 + 13𝑥23 + 7𝑥24 + ℎ2 = 50
14𝑥31 + 9𝑥32 + 16𝑥33 + 5𝑥34 + ℎ3 = 40
8𝑥11 + 9𝑥21 + 14𝑥31 − 𝑒1 = 45
6𝑥12 + 12𝑥22 + 9𝑥23 + 7𝑥24 − 𝑒2 = 20
10𝑥13 + 13𝑥23 + 16𝑥33 − 𝑒3 = 30
9𝑥14 + 7𝑥24 + 5𝑥34 − 𝑒4 = 30
TABLA 1
TABLA 2
0
0
45
/14
0
0
-
15/7
5/7
0
VE
VS
VE
VS
∄
∄
∄
∄
15
8
∄
0
5/2

4. VB Z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 -8 -6 -10 -9 -9 -12 -13 -7 0 0 0 0 0 0 1 0 0 -1 0 40 /-13
H1 0 8 6 10 9 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 35 /0
H2 0 0 0 0 0 9 12 13 7 0 0 0 0 0 1 0 0 0 0 0 50 /13
X31 0 0 0 -5/7 0 0 0 -
13/14
0 1 9/14 0 5/14 0 0 1/14 0 0 0 0 5/7 -10/13
E1 0 8 0 10 0 9 0 13 0 0 -9 0 -5 0 0 -1 -1 0 0 0 35 35/13
E2 0 0 6 0 0 0 12 0 0 0 9 0 0 0 0 0 0 -1 0 0 20 /0
X33 0 0 0 5/8 0 0 0 13/16 0 0 0 1 0 0 0 0 0 0 -
1/16
0 15/8 /13/16
E4 0 0 0 0 9 0 0 0 7 0 0 0 5 0 0 0 0 0 0 -1 30 /0
VB Z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 -8 -6 0 -9 -9 -12 0 -7 0 0 16 0 0 0 1 0 0 -1 0 70 /-
12
H1 0 8 6 10 9 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 35 /0
H2 0 0 0 -10 0 9 12 0 7 0 0 -16 0 0 1 0 0 0 1 0 20 /12
X31 0 0 0 0 0 0 0 0 0 1 9/4 8/7 5/14 0 0 1/4 0 0 0 0 20/7 /0
E1 0 8 0 0 0 9 0 0 0 0 -9 -16 -5 0 0 -1 -1 0 0 0 5 /0
E2 0 0 6 0 0 0 12 0 0 0 9 0 0 0 0 0 0 -1 0 0 20 /12
X23 0 0 0 10/13 0 0 0 1 0 0 0 16/13 0 0 0 0 0 0 -
1/13
0 30/13 /0
E4 0 0 0 0 9 0 0 0 7 0 0 0 5 0 0 0 0 0 0 -1 30 /0
VB z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 -8 -6 -10 -9 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 90 /-10
H1 0 8 6 10 9 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 35 /10
X22 0 0 0 -5/6 0 3/4 1 0 7/12 0 0 -4/3 0 0 1/12 0 0 0 1/12 0 5/3 /-5/6
X31 0 0 0 0 0 0 0 0 0 1 9/4 8/7 5/14 0 0 -
1/14
0 0 0 0 20/7 /0
E1 0 8 0 0 0 9 0 0 0 0 -9 -16 -5 0 0 -1 -1 0 0 0 5 /0
E2 0 0 6 10 0 -9 0 0 -7 0 9 16 0 0 -1 0 0 -1 -1 0 0 /10
X23 0 0 0 10/3 0 0 0 1 0 0 0 16/13 0 0 0 0 0 0 -
1/13
0 30/13 /10/13
TABLA 3
TABLA 5
TABLA 4
VE
VE
VS
VS
VS
VE

5. E4 0 0 0 0 9 0 0 0 7 0 0 0 5 0 0 0 0 0 0 -1 30 /0
VB Z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 -8 -6 0 -9 0 0 100/13 0 0 0 16 0 0 1 1 0 0 -1 0 120 /-9
H1 0 8 6 0 9 0 0 -
100/13
0 0 0 -16 0 1 0 0 0 0 1 0 5 /9
X22 0 0 0 0 0 3/4 1 25/39 7/12 0 0 0 0 0 1/12 0 0 0 0 0 25/6 /0
X31 0 0 0 0 0 0 0 0 0 1 9/4 8/7 5/14 0 0 1/14 0 0 0 0 20/7 /0
E1 0 8 0 0 0 9 0 0 0 0 -9 -16 -5 0 0 -1 -1 0 0 0 5 /0
E2 0 0 6 0 0 -9 0 -
100/13
-7 0 9 0 0 0 -1 0 0 -1 0 0 -30 /0
E13 0 0 0 1 0 0 0 10/13 0 0 0 8/5 0 0 0 0 0 0 -
1/10
0 3 /0
E4 0 0 0 0 9 0 0 0 7 0 0 0 5 0 0 0 0 0 0 -1 30 /9
VB Z X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 X34 H1 H2 H3 E1 E2 E3 E4 Sol
Z 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 125 Z=125
H14 0 8/9 2/3 0 1 0 0 -100/117 0 0 0 -
16/9
-5/8 0 1/9 0 0 0 0 1/9 5/4 H11=0
H22 0 0 0 0 0 3/4 1 35/39 7/12 0 0 0 0 0 1/12 0 0 0 0 0 25/6 X22=4.166
X31 0 0 0 0 0 0 0 0 0 1 9/4 8/7 5/14 0 0 1/14 0 0 0 0 20/7 X13=3
E1 0 8 0 0 0 9 0 0 0 0 -9 -16 -5 0 0 -1 -1 0 0 0 5 E1=-5
E2 0 0 6 0 0 -9 0 -
100/13
-7 0 9 0 0 0 -1 0 0 -1 0 0 -30 E2=-30
X13 0 0 0 1 0 0 0 10/13 0 0 0 8/5 0 0 0 0 0 0 -
1/10
0 3 X31=2.8571
E4 0 -8 -6 0 0 0 0 100/13 7 0 0 16 5 -1 0 0 0 0 -1 -1 25 X14=0.555
TABLA 6
TABLA 7
VE
VS

6. 10(3)+ 9(0.555555556)+ 12(4.166666667)+ 14(2.85714287)= 125
10 (3)+ (0.5555555556)= 35
12 (4.166666667)= 50
14 (2.857142857) = 40
14 (2.857142857) +5 = 45
12 (401666666667) – 30 = 20
10 (3)= 30
9(0.5555555556)+25= 30
COMPROBACIÓN