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Maksimumkan :

Z = 4x1+ 10x2+ 6x3

Dengan Fungsi Kendala :

x1+ 3x2+ 3x3 6

2x1- x2+ 4x3= 4

Ditanya :

Nilai x1, x2, x3 , Z

Jawab :

1. Tambah var dasar

x1+ 3x2+ 3x3+ S1 = 6

2x1- x2+ 4x3+ V1 = 4

2. Ubah Fungsi Tujuan

Z = 4x1+ 10x2+ 6x3- MV1

Nilai Kanan Z harus 0

Z - 4x1- 10x2- 6x3+ MV1

Z X1 X2 X3 S1

Z 1.00 -2m-4 m-10 -4m-6 0.00

A1 0.00 1.00 3.00 3.00 1.00

V1 0.00 2.00 -1.00 4.00 0.00

V1 --> X3

0.00 2.00 -1.00 4.00 0.00

0.00 0.50 -0.25 1.00 0.00

Z

1.00 -2m-4 m-10 -4m-6 0.00

0.00 0.50 -0.25 1.00 0.00

0.00 -2m-3 m+1.5 -4m-6 0.00

1.00 -1.00 -11.50 0.00 0.00

A1 0.00 1.00 3.00 3.00 1.00

0.00 0.50 -0.25 1.00 0.00

0.00 1.50 -0.75 3.00 0.00

0.00 -0.50 3.75 0.00 1.00

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Z X1 X2 X3 S1

Z 1.00 -1.00 -11.50 0.00 0.00

A1 0.00 -0.50 3.75 0.00 1.00

X1 0.00 0.50 -0.25 1.00 0.00

x1--> x2

0.00 0.50 -0.25 1.00 0.00

0.00 -2.00 1.00 -4.00 0.00

Z

1.00 -1.00 -10.67 0.00 0.00

0.00 -2.00 1.00 -4.00 0.00

0.00 21.34 -10.67 42.68 0.00

1.00 -22.34 0.00 -42.68 0.00

A1 0.00 -0.50 3.75 0.00 1.00

0.00 -2.00 1.00 -4.00 0.00

0.00 -7.50 3.75 -15.00 0.00

0.00 7.00 0.00 15.00 1.00

Z X1 X2 X3 S1

Z 1.00 -22.34 0.00 -42.68 0.00

A1 0.00 7.00 0.00 15.00 1.00

X2 0.00 -2.00 1.00 -4.00 0.00

x2 --> x3

0.00 -2.00 1.00 -4.00 0.00

0.00 0.50 -0.25 1.00 0.00

Z 1.00 -22.34 0.00 -42.68 0.00

0.00 0.50 -0.25 1.00 0.00

0.00 -21.34 10.67 -42.68 0.00

1.00 -1.00 -10.67 0.00 0.00

A1 0.00 7.00 0.00 15.00 1.00

0.00 0.50 -0.25 1.00 0.00

0.00 7.50 -3.75 15.00 0.00

0.00 -0.50 3.75 0.00 1.00

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Z X1 X2 X3 S1

Z 1.00 -1.00 -10.67 0.00 0.00

A1 0.00 -0.50 3.75 0.00 1.00

X3 0.00 0.50 -0.25 1.00 0.00

A1-->x1

0.00 -0.50 3.75 0.00 1.00

0.00 0.67 -5.00 0.00 -1.33

Z

1.00 -1.00 -10.67 0.00 0.00

0.00 0.67 -5.00 0.00 -1.33

0.00 0.67m-13.84 - m 103.35 0.00 m - 27.49

1.00 0.67m-12.84 0.00 m+26.16

0.00 -13.78 103.35 0.00 27.56

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V1 NK Indeks

0.00 -4m

0.00 6.00 2.00

1.00 4.00 1.00

1.00 4.00 :4

0.25 1.00

0.00 -4m

0.25 1.00 x - 4m -6

-m-1.5 -4m-6 -

m+1.5 6.00

0.00 6.00

0.25 1.00 x 3

0.75 3.00 -

-0.75 3.00

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V1 NK Indeks

m+1.5 6.00

-0.75 3.00 0.80

0.25 1.00 -4.00

0.25 1.00 :-0.25

-1.00 -4.00

m+2/3 6.00

-1.00 -4.00 x - 10.67

10.67 42.68

m-10 -36.68

-0.75 3.00

-1.00 -4.00 x 3.75

-3.75 -15.00

3.00 18.00

V1 NK Indeks

m-10 -36.68

3.00 18.00 1.20

-1.00 -4.00 1.00

-1.00 -4.00 :-4

0.25 1.00

m-10 -36.68

0.25 1.00 x -42.68

-10.67 -42.68 -

m-20.67 6.00

3.00 18.00

0.25 1.00 x 15

3.75 15.00 -

-0.75 3.00

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V1 NK Indeks

m-20.67 6.00

-0.75 3.00 -4.00

0.25 1.00 4.00

-0.75 3.00 :-0.75

1.00 -4.00

m-20.67 6.00

1.00 -4.00 xm-20.67

m-20.67 -4M+82.68 -

0.00

-20.67 82.68

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Maksimumkan :

Z = 4x1+ 10x2+ 6x3

Dengan Fungsi Kendala :

x1+ 3x2+ 3x3 6

2x1- x2+ 4x3= 4

Ditanya :

Nilai x1, x2, x3 , Z

Jawab :

1. Tambah var dasar

x1+ 3x2+ 3x3+ S1 = 6

2x1- x2+ 4x3+ S2 = 4

2. Ubah Fungsi Tujuan

Z = 4x1+ 10x2+ 6x3- MS2

Nilai Kanan Z harus 0

Z - 4x1- 10x2- 6x3+ MS2

1 -4 -10 -6 0 m 0

0 2 -1 4 0 1 4

0 2M -M 4M 0 m 4M

1 2M-4 -M-10 4M-6 0 0 -4M

Z X1 X2 X3 S1 S2

Z 1 2M-4 -M-10 4M-6 0 0

S1 0.00 1.00 3.00 3.00 1.00 0.00

S2 0.00 2.00 -1.00 4.00 0.00 1.00

S2 0.00 2.00 -1.00 4.00 0.00 1.00

X2 0 -2 1 -4 0 -1

Z 1 2M-4 -M-10 4M-6 0 0

0 -2 1 -4 0 -1

0 2M+20 -M-10 4M+40 0 M+10

1 -24 0 -46 0 -M-10

S1 0.00 1.00 3.00 3.00 1.00 0.00

0 -2 1 -4 0 -1

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0 -6 3 -12 0 -3

0.00 7.00 0.00 15.00 1.00 3.00

Z X1 X2 X3 S1 S2

Z 1 -24 0 -46 0 -M-10

S1 0.00 7.00 0.00 15.00 1.00 3.00

X2 0.00 -2.00 1.00 -4.00 0.00 -1.00

x2 0 -2 1 -4 0 -1

S2 0 2 -1 4 0 1

Z 1 -24 0 -46 0 -M-10

0 2 -1 4 0 1

0 -2M-20 M+10 4M+40 0 M+10

1 2M-4 -M-10 -4M-6 0 0

S1 0.00 7.00 0.00 15.00 1.00 3.00

0 2 -1 4 0 1

0 6 -3 12 0 3

0 1 3 3 1 0

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x M

-

NK Indeks

-4M

6.00 2.00

4.00 1.00

4.00 : -1

-4

-4M

-4 x -M-10

4M+40 -

-8M-40

6.00

-4 x 3

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-12 -

18.00

NK Indeks

-8M-40

18.00 1.20

-4.00 1.00

-4 :-1

4

-8M-40

4 x -M-10

-4M-40 -

-4M

18.00

4 x 3

12 -

6