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