BAB VI - BAB VI. Program Linear Bilangan Bulat

BAB VI
Program Linear Bilangan Bulat

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Masalah 2
Minimumkan Z = 200 x1 + 400 x2

Z = 100 x1 + 90 x2

Dengan pembatas:

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10 x1 + 25 x2 ≥ 100

10 x1 + 7 x2 ≤ 70

3 x1 + 2 x2 ≥ 12

5 x1 + 10 x2 ≤ 50

x1 ≥ 0, x2 ≥ 0

x1 ≥ 0, x2 ≥ 0

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Z = 80 x1 + 100 x2

4 x1 + 2 x 2 ≤ 15
x1 + 5 x 2 ≤ 16
x1 ≥ 0, x 2 ≥ 0

x1 + 5 x 2 ≤ 16

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x1 = 5.38

x1 = 1.82

x1 = 2.388889

x2 = 2.31

x2 = 3.27

x 2 = 2.722222

Z = 746.15

Z = 1,672.73

Z = 463.3333

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x1 = 5

x1 = 2

x1 = 2

x2 = 2

x2 = 3

x2 = 3

Z = 680

Z = tak layak

Z = tak layak

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151

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x1 = 7

x1 = 3, x2 = 3 atau

x1 = 1

x2 = 0

x1 = 5, x2 = 2

x2 = 3

Z = 700

Z = 1,800

Z = 360

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Z = 150 x1 + 175 x2

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6 x1 + 8 x2 ≤ 99
8 x1 + 4 x2 ≤ 87
x1 ≥ 0, x2 ≥ 0

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x1 = 7.5

Nampak disamping bahwa semua solusi bilangan pecah (tidak

x2 = 6.75

bulat) maka harus kita lakukan pencabangan.

Z = 2205

Perhatikan grafik berikut.

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x1 ≤ 7

x1 ≥ 8, x 2 ≥ 0

x1 ≥ 0, x 2 ≥ 7

x2 ≤ 6

8 x1 + 4 x 2 ≤ 87

6 x1 + 8 x 2 ≤ 99

x1 ≥ 0, x2 ≥ 0

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Z1 = 150 . 7 + 175 . 7 = 2170, Z 2 = 150 . 0 + 175 . 12 = 2100
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x1 = 7, x 2 = 7, dengan Z = 2.170

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Max 150x1+175x2
Subject to
6x1+8x2

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