Contoh Soal NLP-Solver.xls

Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Contoh Soal Program Non-Linier dengan Menggunakan Excel Solver oleh Djoko Luknanto

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

sheet: Cover

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Contoh Konsep Program Non-Linier (hal.1-18) 2 2 2 Min Z = a + b + c + 20(a-50) + 20(a+b-100) = 7.500,00 Variables: a b c Z Jawaban: 50,00 50,00 50,00 7.500,00

Fungsi Tujuan: Kendala:

Koefisien 1,00 Koefisien 1,00 0,00 1,00 1,00 1,00 1,00 1,00

1,00 0,00 0,00 1,00

LHS 50,00 >= 100,00 >= 150,00 >=

RHS 50,00 100,00 150,00

Slack 0,00 0,00 0,00

Ref: Djoko Luknanto, Pengantar Optimasi Non-Linier , Jurusan Teknik Sipil, FT UGM, 1996.

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

sheet: NLP01

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Microsoft Excel 9.0 Sensitivity Report Worksheet: [Contoh Soal NLP-Solver.xls]NLP01 Report Created: 23/06/00 6:45:35

Adjustable Cells Final Reduced Cell Name Value Gradient $B$6 Jawaban: a 50,00 0,00 $C$6 Jawaban: b 50,00 0,00 0,00 $D$6 Jawaban: c 50,00 Constraints Cell Name $E$12 LHS $E$11 LHS $E$13 LHS

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

Final Lagrange Value Multiplier 100,00 20,00 50,00 20,00 150,00 100,00

sheet: Sensitivity Report 01

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Microsoft Excel 9.0 Limits Report Worksheet: [Contoh Soal NLP-Solver.xls]NLP01 Report Created: 23/06/00 6:45:35

Target Value Cell Name $E$6 Jawaban: Z 7.500,00

Adjustable Cell Name $B$6 Jawaban: a $C$6 Jawaban: b $D$6 Jawaban: c

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

Value 50,00 50,00 50,00

Lower Limit 50,00 50,00 50,00

Target Result 7500,00 7500,00 7500,00

sheet: Limits Report 01

Upper Target Limit Result #N/A #N/A #N/A #N/A #N/A #N/A

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Contoh Soal 1 Non-Linier (hal. lepas) 2 2 Min Z = X1 + X2 = 37,90 X1 Variables: Jawaban: 2,20

Fungsi Tujuan: Kendala:

X2 5,75

Koefisien 1,00 1,00 Koefisien 1,00 1,00 1,00 1,00

Z 37,90

LHS 25,00 =

RHS 25,00 16,00

Slack 0,00 0,00

Ref: Djoko Luknanto, Pengantar Optimasi Non-Linier , Jurusan Teknik Sipil, FT UGM, 1996.

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

sheet: NLP02

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Microsoft Excel 9.0 Sensitivity Report Worksheet: [Contoh Soal NLP-Solver.xls]NLP02 Report Created: 23/06/00 6:53:55

Adjustable Cells Final Reduced Value Gradient Cell Name $B$6 Jawaban: X1 2,20 0,00 $C$6 Jawaban: X2 5,75 0,00 Constraints Cell Name $D$11 LHS $D$12 LHS

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

Final Lagrange Value Multiplier 25,00 -2,51 16,00 1,93

sheet: Sensitivity Report 02

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Microsoft Excel 9.0 Limits Report Worksheet: [Contoh Soal NLP-Solver.xls]NLP02 Report Created: 23/06/00 6:53:55

Target Cell Name $D$6 Jawaban: Z

Value 37,90

Adjustable Value Cell Name $B$6 Jawaban: X1 2,20 $C$6 Jawaban: X2 5,75

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

Lower Target Limit Result 2,20 37,90 5,75 37,90

sheet: Limits Report 02

Upper Target Limit Result 2,20 37,90 5,75 37,90

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Contoh Soal 2 Non-Linier (hal. lepas) 2 2 Min Z = X1 - X2 + 2X1 + 2X1X2 + X2 = -1,25 X2 X1 Z Variables: Jawaban: -1,00 1,50 -1,25

Ref: Djoko Luknanto, Pengantar Optimasi Non-Linier , Jurusan Teknik Sipil, FT UGM, 1996.

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

sheet: NLP03

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Microsoft Excel 9.0 Sensitivity Report Worksheet: [Contoh Soal NLP-Solver.xls]NLP03 Report Created: 23/06/00 7:00:19

Adjustable Cells Final Reduced Value Gradient Cell Name $B$6 Jawaban: X1 -1,00 0,00 $C$6 Jawaban: X2 1,50 0,00 Constraints NONE

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

sheet: Sensitivity Report 03

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Microsoft Excel 9.0 Limits Report Worksheet: [Contoh Soal NLP-Solver.xls]NLP03 Report Created: 23/06/00 7:00:19

Target Cell Name $D$6 Jawaban: Z

Value -1,25

Adjustable Value Cell Name $B$6 Jawaban: X1 -1,00 $C$6 Jawaban: X2 1,50

file:E:\Kuliah\Optimasi\Non Linier\Contoh Soal NLP-Solver.xls

Lower Target Limit Result #N/A #N/A #N/A #N/A

sheet: Limits Report 03

Upper Target Limit Result #N/A #N/A #N/A #N/A

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Djoko Luknanto

Dasar-dasar Optimasi Non-Linier

Contoh Soal 3 Non-Linier (hal.lepas) 2 2 Min Z = (X1-2) + (X2-2) = 0,80 X2 X1 Variables: Jawaban: 1,60 1,20

Fungsi Tujuan: Kendala:

Koefisien 1,00 1,00 Koefisien 1,00 2,00

Z 0,80

LHS 4,00