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Max z = 3x 1 + 5x 2 s.a 7x 1 + 6x 2 ≤ 100 4x 1 + 11x 2 ≤ 80 x 1 , x 2 ≥ 0 y enteras. (P0) max z = 3x 1 + 5x 2 s.a 7x 1 + 6x 2 ≤ 100 4x 1 + 11x 2 ≤ 80 x 1 , x 2 ≥ 0 (P1) max z = 3x 1 + 5x 2 (P4) max z = 3x 1 + 5x 2 s.a 7x 1 + 6x 2 ≤ 100 s.a 7x 1 + 6x 2 ≤ 100 4x 1 + 11x 2 ≤ 80 4x 1 + 11x 2 ≤ 80 x 2 ≤11 x 2 ≥12 x 1 , x 2 ≥ 0 x 1 , x 2 ≥ 0 (P2) max z = 3x 1 + 5x 2 (P3) max z = 3x 1 + 5x 2 s.a 7x 1 + 6x 2 ≤ 100 s.a 7x 1 + 6x 2 ≤ 100 4x 1 + 11x 2 ≤ 80 4x 1 + 11x 2 ≤ 80 x 2 ≤ 11 x 2 ≤ 11 x 1 ≤3 x 1 ≥ 4 x 1 , x 2 ≥ 0 x 1 , x 2 ≥ 0

# Max z

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### Text of Max z

Max z = 3x1 + 5x2

s.a            7x1 + 6x2    ≤ 100            4x1 + 11x2  ≤ 80

x1, x2 ≥ 0 y enteras.

(P0) max z = 3x1 + 5x2

s.a 7x1 + 6x2 ≤ 100

4x1 + 11x2 ≤ 80

x1, x2 ≥ 0

(P1) max z = 3x1 + 5x2 (P4) max z = 3x1 + 5x2

s.a 7x1 + 6x2 ≤ 100 s.a 7x1 + 6x2 ≤ 100

4x1 + 11x2 ≤ 80 4x1 + 11x2 ≤ 80

x2 ≤11 x2 ≥12

x1, x2 ≥ 0 x1, x2 ≥ 0

(P2) max z = 3x1 + 5x2 (P3) max z = 3x1 + 5x2

s.a 7x1 + 6x2 ≤ 100 s.a 7x1 + 6x2 ≤ 100

4x1 + 11x2 ≤ 80 4x1 + 11x2 ≤ 80

x2 ≤ 11 x2 ≤ 11

x1 ≤3 x1 ≥ 4

x1, x2 ≥ 0 x1, x2 ≥ 0

(P5) max z = 3x1 + 5x2 (P6) max z = 3x1 + 5x2

s.a 7x1 + 6x2 ≤ 100 s.a 7x1 + 6x2 ≤ 100

4x1 + 11x2 ≤ 80 4x1 + 11x2 ≤ 80

x2 ≥ 12 x 2 ≥ 12

x2 ≤ 2 x 1≥3

x1, x2 ≥ 0 x1, x2 ≥ 0

X2 ≤11 x2 ≥12

X2≤3 x2 ≥ 4 x1 ≤2 x1≥3

Solución optima

P0

X1=11.69

X2=3.01

Z0=50.18

P1

X1=11

X2=3.27

Z1= 49.36

P4

X1=12

X2=2.66

Z4= 49.33

P2

X1=11

X2=3

Z2= 48

P3

X1=9

X2=4

Z3= 47

P5

X1=12.57

X2=2

Z4= 47.71

P6

infactible

min z = −5x1 − 8x2

s.a x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45

x1, x2 ≥ 0 y enteros

(P0) min z = −5x1 − 8x2

s.a x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45

X1, x2 ≥ 0

(P1) min z = −5x1 − 8x2 (P2) min z = −5x1 − 8x2

s.a x1 + x2 ≤ 6 s.a x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45 5x1 + 9x2 ≤ 45

x2 ≥ 4 x2 ≤ 3

x1, x2 ≥ 0 x1, x2 ≥ 0

(P3) min z = −5x1 − 8x2 (P4) min z = −5x1 − 8x2

s.a x1 + x2 ≤ 6 s.a x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45 5x1 + 9x2 ≤ 45

x2 ≥ 4 x2 ≥ 4

x1 ≥ 2 x 1 ≤ 1

x1, x2 ≥ 0 x 1, x2 ≥ 0

(P5) min z = −5x1 − 8x2 (P6) min z = −5x1 − 8x2

s.a x1 + x2 ≤ 6 s.a x1 + x2 ≤ 6

5x1 + 9x2 ≤ 45 5x1 + 9x2 ≤ 45

x2 ≥ 4 x 2 ≥ 4

x1 ≤ 1 x 1 ≤ 1

x2 ≤ 4 x 2 ≥ 5

x1, x2 ≥ 0 x1, x2 ≥ 0

x2 ≥ 4 x2 ≤ 3

x1 ≥ 2 x1 ≤ 1

x2 ≤ 4 x2 ≥ 5

solución optima

P0

X1=2.25

X2=3.75

Z0=41.25

P1

X1=1.8

X2=4

Z1= -41

P2

X1=3

X2=3

Z2= -39

P4

X1=1

X2=4.4

Z4= -40.5

P3

infactible

P5

X1=1

X2=4

Z5= -37

P6

X1=0

X2=5

Z6= -40

Max z = 8x1 + 10x2

s.a            4x1 + 6x2    ≤ 24            8x1 + 3x2  ≤ 24x1, x2 ≥ 0 y enteras.

(P0) max z = 8x1 + 10x2

s.a 4x1 + 6x2 ≤ 24

8x1 + 3x2 ≤ 24

x1, x2 ≥ 0

(P1) max z = 8x1 + 10x2 (P2) max z = 8x1 + 10x2

s.a 4x1 + 6x2 ≤ 24 s.a 4x1 + 6x2 ≤ 24

8x1 + 3x2 ≤ 24 8x1 + 3x2 ≤ 24

x2 ≥3 x2 ≤2

x1, x2 ≥ 0 x1, x2 ≥ 0

(P3) max z = 8x1 + 10x2 (P4) max z = 8x1 + 10x2

s.a 4x1 + 6x2 ≤ 24 s.a 4x1 + 6x2 ≤ 24

8x1 + 3x2 ≤ 24 4x1 + 11x2 ≤ 80

x2 ≥3 x2 ≥ 3

x1 ≤1 x1 ≥ 2

x1, x2 ≥ 0 x1, x2 ≥ 0

(P5) max z = 8x1 + 10x2 (P6) max z = 8x1 + 10x2

s.a 4x1 + 6x2 ≤ 24 s.a 4x1 + 6x2 ≤ 24

8x1 + 3x2 ≤ 24 8x1 + 3x2 ≤ 24

x2 ≥ 3 x2 ≥ 3

x1 ≤ 1 x1 ≤ 1

x2≤ 3 x2≥4

x1, x2 ≥ 0 x1, x2 ≥ 0

X2 ≥3 x2 ≤2

X1≤1 x1 ≥ 2

X2≤ 3 x2≥ 4

Solución optima

P0

X1=2

X2=8/3

Z0=128/3

P1

X1=1.5

X2=3

Z1= 42

P2

X1=2.5

X2=2

Z2= 38

P3

X1=1

X2=10/3

Z3= 124/3

P4

infactible

P5

X1=1

X2=3

Z5= 38

P6

X1=0

X2=4

Z6= 40

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