tugas - kelompok 2
DESCRIPTION
metode optimasiTRANSCRIPT
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METODE OPTIMASI TUGAS
KELOMPOK 2:
1. Eko Dwi Nugroho (14/372086/PPA/4643)
2. Arief Ichwani (14/372962/PPA/4746)
3. Ari Kusuma Wardana (14/372201/PPA/4651)
4. Ersyaf Ikhsanul Fikri (14/371694/PPA/4597)
5. Adityas Rucitra Pradipta (14/372090/PPA/4644)
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Soal:
Max z = x1 + x2
s.t. 2x1 - x2 3 3x1 + x2 3.5 x1 + x2 1
x1 , x2 0
Solusi:
Langkah 1:
z - x1 - x2 - 0e1 + 0s2 + 0s3 = 0
2x1 + x2 - e1 = 3
3x1 + x2 + s2 = 7
2
x1 + x2 + s3 = 1
x1 , x2 , e1 , s2 , s3 0
Langkah 2:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3
2 0 3 1 0 1 0
7
2
3 0 1 1 0 0 1 1
Langkah 3:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3
2 0 3 1 0 1 0
7
2
3 0 1 1 0 0 1 1
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Langkah 4:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3 3
1= 3
2 0 3 1 0 1 0 7
2
721
= 7
2
3 0 1 1 0 0 1 1 1
1= 1
Langkah 5:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3 3
1= 3
2 0 3 1 0 1 0 7
2
721
= 7
2
3 0 1 1 0 0 1 1 1
1= 1
Langkah 6:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3
2 0 3 1 0 1 0 7
2
3 0 1 1 0 0 1 1
Langkah 7:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
b0 = b0 + b3 0 1 0 0 0 0 1 1
b1 = b1 b3 1 0 1 0 -1 0 0 2
b2 = b2 b3 2 0 2 0 0 1 -1 5
2
b3 = b3 3 0 1 1 0 0 1 1
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Langkah 8:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 0 0 0 0 1 1
1 0 1 0 -1 0 0 2
2 0 2 0 0 1 -1 5
2
3 0 1 1 0 0 1 1
Sehingga: x1 = 0
x2 = 1
e1 = 0
s2 = 5
2
s3 = 0
z2 = 1
Hasil:
Jadi z = x1 + x2 - 0e1 + 0s2 + 0s3
= 0 + 1 - 0 0 + 0 5
2 + 0 0
= 1
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Langkah 3:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3
2 0 3 1 0 1 0
7
2
3 0 1 1 0 0 1 1
Langkah 4:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3 3
1= 3
2 0 3 1 0 1 0 7
2
721
= 7
2
3 0 1 1 0 0 1 1 1
1= 1
Langkah 5:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3 3
2
2 0 3 1 0 1 0 7
2
723
= 7
6
3 0 1 1 0 0 1 1 1
1= 1
Langkah 6:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 -1 -1 0 0 0 0
1 0 2 1 -1 0 0 3
2 0 3 1 0 1 0 7
2
3 0 1 1 0 0 1 1
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Langkah 7:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
b0 = b0 + b3 0 1 0 0 0 0 1 1
b1 = b1 2b3 1 0 0 -1 -1 0 -2 1
b2 = b2 3b3 2 0 0 -2 0 1 -3 1
2
b3 = b3 3 0 1 1 0 0 1 1
Langkah 8:
OPERASI BARIS z x1 x2 e1 s2 s3 RHS CEK
RASIO
0 1 0 0 0 0 1 1
1 0 0 -1 -1 0 -2 1
2 0 0 -2 0 1 -3 1
2
3 0 1 1 0 0 1 1
Sehingga: x1 = 1
x2 = 0
e1 = 0
s2 = 1
2
s3 = 0
z2 = 1
Hasil:
Jadi z = x1 + x2 - 0e1 + 0s2 + 0s3
= 1 + 0 - 0 0 + 0 1
2 + 0 0
= 1