exercícios simplex puccini

8/18/2019 Exercícios Simplex Puccini

1/22

0

-W 0 0 0 0 1 1

-Z 3 2 0 0 0 0

1 1 -1 0 1 0

2 1 0 -1 0 1

1

-W -3 -2 1 1 0 0

-Z 3 2 0 0 0 0

1 1 -1 0 1 0

2 1 0 -1 0 1

2

-W 0 -0.5 1 -0.5 0 1.5

-Z 0 0.5 0 1.5 0 -1.5

0 0.5 -1 0.5 1 -0.5

1 0.5 0 -0.5 0 0.5

3

-W 0 0 0 0 1 1

-Z 0 -1 3 0 -3 0

0 1 -2 1 2 -1

1 1 -1 0 1 0

b Razão

X1

X2

X3

X4

X5

X6

L0

L1

L2

X3

L3

X4

X1

X2

X3

X4

X5

X6

L0

L1

L2

X3

L3

X4

X1

X2

X3

X4

X5

X6

L0

L1

L2

X3

L3

X1

X1

X2

X3

X4

X5

X6

L0

L1

L2

X4

L3 X1

X1

X2

X3

X4

============ →í


2/22

4

-Z 0 -1 3 0 -15

0 1 -2 1 3 3

1 1 -1 0 5

b Razão

5

-Z 0 0 1 1 -12

0 1 -2 1 3

1 0 1 -1 2

L0

L1

X4

L2

X1

X1

X2

X3

X4

L0

L1

X2

L2

X1

=12

_1=2 _2=3

Solução:


3/22

b

0

0

5

7

b Razão

-12

0

5 5

7 3.5

b Razão

-1.5

-10.5

1.5 3

3.5 -7

b Razão

0

-15

3

5

.= _1+ 3 〖 2〗 _2

_1+ _2≥5

〖 2 〗 _1+ _2 ≥7

→ ^′ − )_ =_ (_+_


4/22


5/22

− + _1+ _2=03 2

_1+ _2 _3− _ + 5=5

〖 2 〗 _1+ _2 _4 _6=7− +

min〖=〖 _5+〗 _6 〗

− +〖 _5+〗 _6=0


6/22


7/22

0

-W 0 0 0 0 0 1

-Z -7 -9 0 0 0 0

-1 1 1 0 0 0

3 5 0 1 0 0

5 4 0 0 -1 1

1

-W -7 -10 -1 -1 1 0

-Z -7 -9 0 0 0 0

-1 1 1 0 0 0

3 5 0 1 0 0

5 4 0 0 -1 1

2

-W -17 0 9 -1 1 0

-Z -16 0 9 0 0 0

-1 1 1 0 0 0

8 0 -5 1 0 0

9 0 -4 0 -1 1

3

-W 0 0 -1.625 1.125 1 0

-Z 0 0 -1 2 0 0

0 1 0.375 0.125 0 0

1 0 -0.625 0.125 0 0

0 0 1.625 -1.125 -1 1

X1

X2

X3

X4

X5

X6

L0

L1

L2

X3

L3

X4

L4

X5

X1

X2

X3

X4

X5

X6

L0

L1

L2

X3

L3

X4

L4

X5

X1

X2

X3

X4

X5

X6

L0

L1

L2

X2

L3

X4

L4

X5

X1

X2

X3

X4

X5

X6

L0

L1

L2

X2

L3

X1

L4

X5


8/22

4

-W 0 0 0 0 0 1

-Z 0 0 0 1.3076923 -0.615385 0.6153846

0 1 0 0.3846154 0.2307692 -0.230769

1 0 0 -0.307692 -0.384615 0.3846154

0 0 1 -0.692308 -0.615385 0.6153846

b

5

-Z 0 0 0 1.3076923 -0.615385 31.923077

0 1 0 0.3846154 0.2307692 1.1538462

1 0 0 -0.307692 -0.384615 3.0769231

0 0 1 -0.692308 -0.615385 3.9230769

b

5

-Z 0 2.6666667 0 2.3333333 0 35

0 4.3333333 0 1.6666667 1 5

1 1.6666667 0 0.3333333 0 5

0 2.6666667 1 0.3333333 0 7

X1

X2

X3

X4

X5

X6

L0

L1

L2

X2

L3

X1

L4

X3

X1

X2

X3

X4

X5

L0

L1

X2

L2

X1

L3

X3

X1

X2

X3

X4

X5

L0

L1

X5

L2

X1

L3

X3

============ →í

=35 _1=5 _2=0 _3=7 _4=0 _5=5

Solução:


9/22

b

0

0

2

15

20

b Razão

-37

0

2 2

15 3

20 5

b Razão

-17

18

2

5 0.625

12 1.333333

b Razão

-6.375

28

2.625 7

0.625

6.375 3.923077

.= _1+ ! 〖 "〗 _2

_1− _2≥−2

〖 3 〗 _1+〖 5 〗 _2≤15

〖 5 〗 _1+〖 4 〗 _2≤20

→ ^′ − )_ =_ (_#+_+_


10/22

b Razão

0

31.923077

1.1538462

3.0769231

3.9230769

Razão

5

Razão


11/22

− _1−! 〖 "〗 _2=0

− _1+ _2 _3+ =2

〖 3 〗 _1+〖 5 〗 _2 _4=1+5

〖 5 〗 _1+〖 4 〗 _2 _5 _ − +6=20

min〖 _6= 〗− + _6 =0


12/22


13/22

b

0

Z -3 -2 -5 0 0 0

2 3 4 1 0 10

5 6 2 0 1 12

b

1

Z -0.5 1.75 0 1.25 0 12.5

0.5 0.75 1 0.25 0 2.5

4 4.5 0 -0.5 1 7

b

2

Z 0 2.3125 0 1.1875 0.125 13.375

0 0.1875 1 0.3125 -0.125 1.625

1 1.125 0 -0.125 0.25 1.75

X1

X2

X3

X4

X5

L0

L1

X4

L2

X5

X1

X2

X3

X4

X5

L0

L1

X3

L2

X5

X1

X2

X3

X4

X5

L0

L1

X3

L2

X1


14/22

Razão

2.5

6

Razão

5

1.75

Razão

. = _1+ 3 2 _2+ _3$ s.a.

2 _1+ 3 _2 + _3% ≤105 _1+ 6 _2 + _3≤122

_1 _2 _3≥0& &

− _1−3 2 _2− _3=0$ 2 _1+ 3 _2 + _3 _4=% + 10 5 _1+ 6 _2 + _32 + _5=12

_1 _2 _3& & _ & 4 _ & 5≥0

=13,375

_1=1,75 _3=1,625 _2 _4 _5=0= =

Solução:


15/22

0

-Z 0 0 0 1 1 1

-1 0 -2 1 0 0

2 -3 1 0 1 0

2 -5 6 0 0 1

1

-Z -3 8 -5 0 0 0

-1 0 -2 1 0 0

2 -3 1 0 1 0

2 -5 6 0 0 1

2

-Z -1.333333 3.8333333 0 0 0 0.8333333

-0.333333 -1.666667 0 1 0 0.3333333

1.6666667 -2.166667 0 0 1 -0.166667

0.3333333 -0.833333 1 0 0 0.1666667

3

-Z 0 2.1 0 0 0.8 0.7

0 -2.1 0 1 0.2 0.3

1 -1.3 0 0 0.6 -0.1

0 -0.4 1 0 -0.2 0.2

X1

X2

X3

X4

X5

X6

L0

L1

X4

L2

X5

L3

X6

X1

X2

X3

X4

X5

X6

L0

L1

X4

L2

X5

L3

X6

X1

X2

X3

X4

X5

X6

L0

L1

X4

L2

X5

L3

X3

X1

X2

X3

X4

X5

X6

L0

L1

X4

L2

X1

L3 X3


16/22

b

0

5

3

5

b Razão

-13

5

3 3

5 0.833333

b Razão

-8.833333

6.6666667

2.1666667 1.3

0.8333333 2.5

b Razão

-7.1

7.1

1.3

0.4

. _4 = + _5 _6+ s.a.

− _1−2 _ 3 _4=5+ 2 _1 −3 _2 _3 _5+ +

_1−2 5 _ _1 _2 _3,& & _ 4 _ & 5 _ &

Solução:

− _4+ + _5 _6=+− _1−2 _ 3 _4=+2 _1 −3 _2 _3+ +

_1−2 5 _2+ 6 _3

→ ^′ − )_ =_ (_#+_+_

=7,1 _1=1, _3=0, _4=7, _2 _5=

Solução:


17/22

3

+6 _3 _ + 6=5≥0

,

5=3

_ 6=5

_6=0=


18/22

b

0

Z -2 -3 0 0 0 0

-1 2 1 0 0 4

1 1 0 1 0 6

1 3 0 0 1 9

b

1

Z -3.5 0 1.5 0 0 6

-0.5 1 0.5 0 0 2

1.5 0 -0.5 1 0 4

2.5 0 -1.5 0 1 3

b

2

Z 0 0 -0.6 0 1.4 10.2

0 1 0.2 0 0.2 2.6

0 0 0.4 1 -0.6 2.2

1 0 -0.6 0 0.4 1.2

b

3

Z 0 0 0 1.5 0.5 13.5

0 1 0 -0.5 0.5 1.5

0 0 1 2.5 -1.5 5.5

1 0 0 1.5 -0.5 4.5

X1

X2

X3

X4

X5

L0

L1

X4

L2

X5

L3

X6

X1

X2

X3

X4

X5

L0

L1

X2

L2

X5

L3

X6

X1

X2

X3

X4

X5

L0

L1

X2

L2

X5

L3

X1

X1

X2

X3

X4

X5

L0

L1

X2

L2

X3

L3 X1


19/22

Razão

2

6

3

Razão

2.666667

1.2

Razão

13

5.5

Razão

. = _1+ _2 2 3 s.a.

− _1+ _22 ≤4 _1 _2≤6+

_1+ _2≤93 _1 _2≥0&

Solução:

− _1−2 〖 3〗 _2=0− _1+ _2 _3=42 +

_1 _2 _4=6+ + _1+ _2 _5=93 +

=13,5 _1=4,5 _2=1,5 _3=5,5 _4 _5=0=

Solução:


20/22


21/22

0

Z -4 -2 2 -2 0 0

1 1 -1 2 1 0

4 -5 5 3 0 1

1

Z 0 2 -2 6 4 0

1 1 -1 2 1 0

0 -9 9 -5 -4 1

2

Z 0 0 0 4.8888889 3.1111111 0.2222222

1 0 0 1.4444444 0.5555556 0.1111111

0 -1 1 -0.555556 -0.444444 0.1111111

X1

X'2

X''2

X3

X4

X5

L0

L1

X4

L2

X5

X1

X'2

X''2

X3

X4

X5

L0

L1

X1

L2

X5

X1

X'2

X''2

X3

X4

X5

L0

L1

X1

L2

X''2


22/22

b Razão

0

4 4

30 7.5

b Razão

16

4

14 1.555556

b Razão

19.111111

5.5555556

1.5555556

. = _1+ _2+ _3 % 2 2 s.a.

_1 _2+ _3+ 2 ≤4

〖 %〗 _1− _2+ _3≤30$ 3

_1≥0 _3≥0' _2 ç )*) ,

Solução:− _1− _2^′+ _2^′′− _3=0% 2 2 2

_1 _2^′ _2^′′+ _3 _4=+ − 2 + 4

〖 %〗 _1− _2^′+ _2^′′+ _3 _5=30$ $ 3 + =19,11 _1=5,5556 _2 _2^′ _2^′′=1,5556= − _3 _4 _5=0= =

exercícios simplex puccini

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