Tugas 2 Riset Operasi

Tugas II
Selesaikan tabel simpleks berikut hingga mencapai nilai optimal

Cj
80
100
0
0
0

Basis

X1
X2
S1
S2
S3
bj
S1

3
2
1
0
0
18
S2

2
4
0
1
0
20
S3

0
1
0
0
0
4
Zj






Cj-Zj









Penyelesaian:



Cj
80
100
0
0
0

Basis

X1
X2
S1
S2
S3
bj
S1
0
3
2
1
0
0
18
S2
0
2
4
0
1
0
20
S3
0
0
1
0
0
0
4
Zj
0
0
0
0
0

Cj-Zj
80
100
0
0
0

Ratio
18/2 = 9 ratio terbesar
20/4 = 5
4/1 = 4 → BK (baris khusus diambil dari nilai bj dengan ratio terkecil)
·         KK (kolom khusus) = 100 (nilai terbesar dari Cj)
·         Pivot = 1 (didapatkan setelah memplotingkan nilai KK dan BK)
·         Faktor pengali = 2 (diambil dari ratio paling besar yaitu 9)




Cj
80
100
0
0
0

Basis

X1
X2
S1
S2
S3
bj
S1
0
3
0
1
0
0
10
S2
0
2
2
0
1
0
12
S3
100
0
1
0
0
0
4
Zj
0
100
0
0
0
400
Cj-Zj
80
0
0
0
0

Ratio
10/3 = 3,33 → BK
12/2 = 6
4/0 = ∞ → ratio terbesar
·         Pivot = 3
·         Faktor pengali = 0





Cj
80
100
0
0
0

Basis

X1
X2
S1
S2
S3
bj
X1
80
1
0
1/3
0
0
10/3
S2
0
2
2
0
0
0
12
S3
100
0
1
0
0
0
4
Zj
80
100
80/3
0
0
666,67
Cj-Zj
0
0
-80/30
0
0

                                                                       

Karena (Cj-Zj) ≤ 0 , maka sudah di dapatkan nilai yang optimal dengan hasil 666,67.


Perhitungan tabel 2
S1
baris (1,1) = 3 ─ 2.0 = 3
baris (1,2) = 2 ─ 2.1 = 0
baris (1,3) = 1 ─ 2.0 = 1
baris (1,4) = 0 ─ 2.0 = 0
baris (1,5) = 0 ─ 2.0 = 0
baris (1,6) = 18 ─ 2.4 = 10

S2
baris (2,1) = 2 ─ 2.0 = 2
baris (2,2) = 4 ─ 2.1 = 2
baris (2,3) = 0 ─ 2.0 = 0
baris (2,4) = 1 ─ 2.0 = 1
baris (2,5) = 0 ─ 2.0 = 0
baris (2,6) = 20 ─ 2.4 = 12

Perhitungan tabel 3
X2
baris (3,1) = 0 ─ 0.1 = 0
baris (3,2) = 1 ─ 0.0 = 1
baris (3,3) = 0 ─ 0.0,33 = 0
baris (3,4) = 0 ─ 0.0 = 0
baris (3,5) = 0 ─ 0.0 = 0
baris (3,6) = 4 ─ 0.3,33 = 4

S2
baris (2,1) = 2 ─ 0.1 = 2
baris (2,2) = 2 ─ 0.0 = 2
baris (2,3) = 0 ─ 0.0,33 = 0
baris (2,4) = 1 ─ 0.0 = 1
baris (2,5) = 0 ─ 0.0 = 0
baris (2,6) = 12 ─ 0.3,33 = 12


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