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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
8/18/2019 Exercícios Simplex Puccini
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:
8/18/2019 Exercícios Simplex Puccini
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
→ ^′ − )_ =_ (_+_
8/18/2019 Exercícios Simplex Puccini
4/22
8/18/2019 Exercícios Simplex Puccini
5/22
− + _1+ _2=03 2
_1+ _2 _3− _ + 5=5
〖 2 〗 _1+ _2 _4 _6=7− +
min〖=〖 _5+〗 _6 〗
− +〖 _5+〗 _6=0
8/18/2019 Exercícios Simplex Puccini
6/22
8/18/2019 Exercícios Simplex Puccini
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
8/18/2019 Exercícios Simplex Puccini
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:
8/18/2019 Exercícios Simplex Puccini
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
→ ^′ − )_ =_ (_#+_+_
8/18/2019 Exercícios Simplex Puccini
10/22
b Razão
0
31.923077
1.1538462
3.0769231
3.9230769
Razão
5
Razão
8/18/2019 Exercícios Simplex Puccini
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
8/18/2019 Exercícios Simplex Puccini
12/22
8/18/2019 Exercícios Simplex Puccini
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
8/18/2019 Exercícios Simplex Puccini
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:
8/18/2019 Exercícios Simplex Puccini
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
8/18/2019 Exercícios Simplex Puccini
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:
8/18/2019 Exercícios Simplex Puccini
17/22
3
+6 _3 _ + 6=5≥0
,
5=3
_ 6=5
_6=0=
8/18/2019 Exercícios Simplex Puccini
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
8/18/2019 Exercícios Simplex Puccini
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:
8/18/2019 Exercícios Simplex Puccini
20/22
8/18/2019 Exercícios Simplex Puccini
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
8/18/2019 Exercícios Simplex Puccini
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= =