Max z
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Transcript 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
