Problema a g
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PROBLEMA A
Max z=60 x1+50 x2
s . a2x1+4 x2≤48→2 x1+4 x2=48→x1=24 x2=12
3 x1+2 x2≤36→3x1+2 x2=36→x1=12 x2=18
x1 , x2≥0
Max z=60 (6 )+50 (9 )=810Rectas de intersección 2 x1+4 x2=48
3 x1+2 x2=36
Punto optimox1=6
x2=9 SOLUCION ÓPTIMA
PROBLEMA B
Max z=15 x1+18 x2
s . a x1+x2≤50000→x1+x2=50000→x1=50000 x2=50000
x1≥15000→x1=15000→x1=15000x2=¿
x2≥10000→x2=10000→x1=x2=10000
x2≤25000→x2=25000→x1=x2=25000
x1 , x2≥0
Max z=15 (25000 )+18 (25000 )=825000
Punto optimox1=25000
x2=25000
SOLUCION ÓPTIMA
Rectas de intersección
x1+ x2=50000
x2=25000
PROBLEMA C
Min z=10000x1+8000 x2
s . a3x1+2 x2≤84→3x1+2 x2=84→x1=28x2=42
x1≥8→x1=8→x1=8 x2=¿
x2≥10→x2=10→x1=x2=10
x1+ x2≥25→x1+x2=25→x1=25 x2=25
x1 , x2≥0
Min z=10000 (8 )+8000 (17 )=216000
Punto optimox1=8
x2=17
SOLUCION ÓPTIMA
Rectas de intersección
x1=8
x1+ x2=25
PROBLEMA D
MIN z=10x1+30 x2
s . a x1+5 x2≥15→x1+5 x2=15→x1=15 x2=3
5 x1+x2≥15→5x1+x2=15→x1=3 x2=15
x1 , x2≥0
Min z=60 (6 )+50 (9 )=810
Punto optimox1=2.5
x2=2.5SOLUCION ÓPTIMA
Rectas de intercesión
x1+5x2=15
5 x1+x2=15
PROBLEMA E
MIN z=100x1+300 x2
s . a8 x1+40 x2≤800→8 x1+40 x2=800→x1=100 x2=20
5 x1+10 x2≤320→5 x1+10 x2=320→x1=64 x2=32
x1 , x2≥0
Max z=100 (40 )+300 (12 )=7600
Punto optimox1=40
x2=12SOLUCION ÓPTIMA
Rectas de intersecion
8 x1+40 x2=800
5 x1+10 x2=320
PROBLEMA F
Max z=30 x1+50 x2
s . a x1+3 x2≤200→x1+3 x2=200→x1=200 x2=66.7
x1+ x2≤100→x1+x2=100→x1=100 x2=100
x1≥20→x1=20→x1=20 x2=¿
x2≥10→x2=10→x1=x2=10
x1 , x2≥0
Max z=30 (50 )+50 (50 )=4000
Punto optimox1=50
x2=50
SOLUCION ÓPTIMA
Rectas de intersección
x1+3x2=200
x1+ x2=100
PROBLEMA G
Max z=6.5 x1+7 x2
s . a2x1+3 x2≤600→2 x1+3 x2=600→x1=300x2=200
x1+ x2≤500→x1+x2=500→x1=500 x2=500
2 x1+x2≤400→2 x1+x2=400→x1=200 x2=400
x1 , x2≥0
Max z=6.5 (150 )+7 (100 )=1675Rectas de intersección 2 x1+3 x2=600
2 x1+x2=400
Punto optimox1=150
x2=100
SOLUCION ÓPTIMA