Penerapan Metode Branch and Bound dalam Menentukan Jumlah Produksi Optimum pada CV. Keris Sakti
Lampiran 1. Perhitungan Simpleks Awal
Iterasi 0
Basis / C
s1
0
s2
0
s3
0
s4
0
s5
0
s6
0
s7
0
s12
M
s13
M
s14
M
s15
M
Zj - Cj
13000
x1
1.2
0.6
1
1
0
0
0
1
0
0
0
M-13000
10000
x2
1.1
0.4
0.75
0
1
0
0
0
1
0
0
M-10000
12000
x3
1
0.6
1
0
0
1
0
0
0
1
0
M-12000
10000
x4
1
0.4
0.75
0
0
0
1
0
0
0
1
M-10000
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
0
0
0
0
-1
0
0
0
-M
0
s9
0
0
0
0
0
0
0
0
-1
0
0
-M
0
s10
0
0
0
0
0
0
0
0
0
-1
0
-M
0
s11
0
0
0
0
0
0
0
0
0
0
-1
-M
M
s12
0
0
0
0
0
0
0
1
0
0
0
0
M
s13
0
0
0
0
0
0
0
0
1
0
0
0
M
s14
0
0
0
0
0
0
0
0
0
1
0
0
M
s15
0
0
0
0
0
0
0
0
0
0
1
0
Universitas Sumatera Utara
B
55000
12000
4160
1600
900
1250
875
1575
850
1245
800
4470M
Iterasi 1
13000
x1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13000
1
M
0
M
0
M
0
Basis / C
s1
s2
s3
s4
s5
s6
s7
x1
s13
s14
s15
Zj - Cj
0
10000
x2
1.1
0.4
0.75
0
1
0
0
0
1
0
0
12000
x3
1
0.6
1
0
0
1
0
0
0
1
0
10000
x4
1
0.4
0.75
0
0
0
1
0
0
0
1
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
0
s9
0
0
0
0
0
0
0
0
-1
0
0
0
s10
0
0
0
0
0
0
0
0
0
-1
0
0
s11
0
0
0
0
0
0
0
0
0
0
-1
M
s13
0
0
0
0
0
0
0
0
1
0
0
M
s14
0
0
0
0
0
0
0
0
0
1
0
M
s15
0
0
0
0
0
0
0
0
0
0
1
M-10000
M-12000
M-10000
0
0
0
0
0
0
0
-13000
-M
-M
-M
0
0
0
B
53110
11055
2585
25
900
1250
875
1575
850
1245
800
2895M+20475000
Universitas Sumatera Utara
Iterasi 2
13000
10000
12000
x1
x2
x3
s1
0
0
1.1
0
s2
0
0
0.4
0
s3
0
0
0.75
0
s4
0
0
0
0
s5
0
0
1
0
s6
0
0
0
0
s7
0
0
0
0
x1 13000
1
0
0
s13
M
0
1
0
x3 12000
0
0
1
s15
M
0
0
0
Zj - Cj
0
M-10000
0
Basis / C
10000
x4
1
0.4
0.75
0
0
0
1
0
0
0
1
M-10000
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
0
0
0
0
-1
0
0
-M
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
0
0
0
0
0
0
0
0
0
0
-1
-M
M
s13
0
0
0
0
0
0
0
0
1
0
0
0
M
s15
0
0
0
0
0
0
0
0
0
0
1
0
B
51865
10308
1340
25
900
5
875
1575
850
1245
800
1650M+35415000
Universitas Sumatera Utara
Iterasi 3
13000
10000
12000
x1
x2
x3
s1
0
0
1.1
0
s2
0
0
0.4
0
s3
0
0
0.75
0
s4
0
0
0
0
s5
0
0
1
0
s6
0
0
0
0
s7
0
0
0
0
x1 13000
1
0
0
s13
M
0
1
0
x3 12000
0
0
1
x4 10000
0
0
0
Zj - Cj
0
M-10000
0
Basis / C
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
0
0
0
0
-1
0
0
-M
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
M
s13
0
0
0
0
0
0
0
0
1
0
0
0
B
51065
9988
740
25
900
5
75
1575
850
1245
800
850M+43415000
Universitas Sumatera Utara
Iterasi 4
Basis / C
s1
s2
s3
s4
s5
s6
s7
x1
x2
x3
x4
0
0
0
0
0
0
0
13000
10000
12000
10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
-13000
0
s9
1.1
0.4
0.75
0
1
0
0
0
-1
0
0
-10000
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50130
9648
102.5
25
50
5
75
1575
850
1245
800
51915000
Universitas Sumatera Utara
Iterasi 5
Basis / C
s1
s2
s3
s8
s5
s6
s7
x1
x2
x3
x4
0
0
0
0
0
0
0
13000
10000
12000
10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
-1.2
-0.6
-1
1
0
0
0
1
0
0
0
13000
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
1.1
0.4
0.75
0
1
0
0
0
-1
0
0
-10000
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50100
9633
77.5
25
50
5
75
1600
850
1245
800
52240000
Universitas Sumatera Utara
Iterasi 6
Basis / C
s1
0
s2
0
s3
0
s8
0
s5
0
s10
0
s7
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
-1.2
-0.6
-1
1
0
0
0
1
0
0
0
13000
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
-1
-0.6
-1
0
0
1
0
0
0
1
0
12000
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
1.1
0.4
0.75
0
1
0
0
0
-1
0
0
-10000
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50095
9630
72.5
25
50
5
75
1600
850
1250
800
52300000
Universitas Sumatera Utara
Iterasi 7
Basis / C
s1
0
s2
0
s3
0
s8
0
s9
0
s10
0
s7
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
s4
s5
s6
-1.2
-1.1
-1
-0.6
-0.4
-0.6
-1
-0.75
-1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
13000 10000 12000
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50040
9610
35
25
50
5
75
1600
900
1250
800
52300000
Universitas Sumatera Utara
Iterasi 8
Basis / C
s1
0
s2
0
s3
0
s8
0
s9
0
s10
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
s4
s5
s6
s7
-1.2
-1.1
-1
-1
-0.6
-0.4
-0.6
-0.4
-1
-0.75
-1
-0.75
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
13000 10000 12000 10000
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49965
9580
-21.25
25
50
5
75
1600
900
1250
875
52300000
Universitas Sumatera Utara
Iterasi 9
Basis / C
s1
0
s2
0
s5
0
s8
0
s9
0
s10
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.4667
-0.5333
-1.3333
0
1.33333
0
0
0
1.33333
0
0
0
0
s4
0.26667
-0.0667
1.33333
1
-1.3333
0
0
1
-1.3333
0
0
-13333
0
s5
0
0
1
0
0
0
0
0
0
0
0
0
0
s6
0.46667
-0.0667
1.33333
0
-1.3333
1
0
0
-1.3333
1
0
-13333
0
s7
0.1
0
1
0
-1
0
1
0
-1
0
1
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49996.17
9591.333
28.33333
25
21.66667
5
75
1600
871.6667
1250
875
53266667
Universitas Sumatera Utara
Iterasi 10
Basis / C
s1
0
s2
0
s5
0
s4
0
s9
0
s10
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.4667
-0.5333
-1.3333
0
1.33333
0
0
0
1.33333
0
0
13333
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
1
0
0
0
0
0
0
0
0
0
0
s6
0.46667
-0.0667
1.33333
0
-1.3333
1
0
0
-1.3333
1
0
-13333
0
s7
0.1
0
1
0
-1
0
1
0
-1
0
1
0
0
s8
-0.2667
0.0667
-1.3333
1
1.3333
0
0
-1
1.3333
0
0
333
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49989.5
9593.001
-4.99992
25
54.99917
5
75
1575
904.9992
1250
875
53274992
Universitas Sumatera Utara
Iterasi 11
Basis / C
s1
0
s2
0
s5
0
s4
0
s9
0
s6
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.4667
-0.5333
-1.3333
0
1.33333
0
0
0
1.33333
0
0
13333
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
1
0
0
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0.1
0
1
0
-1
0
1
0
-1
0
1
0
0
s8
-0.2667
0.0667
-1.3333
1
1.3333
0
0
-1
1.3333
0
0
333
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
-0.4667
0.0667
-1.3333
0
1.3333
1
0
0
1.3333
-1
0
1333
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49987.17
9593.334
-11.6666
25
61.66567
5
75
1575
911.6657
1245
875
53281657
Universitas Sumatera Utara
Iterasi 12
Basis / C
s1
0
s2
0
s3
0
s4
0
s9
0
s6
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
-1.1001
-0.4
-0.75
0
1
0
0
0
1
0
0
10000
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
-1.0001
-0.4
-0.75
0
0
0
1
0
0
0
1
10000
0
s8
1.20006
0.60001
1.00002
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
1.00006
0.60001
1.00002
0
0
1
0
0
0
-1
0
-12000
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
50000
9598.001
8.750144
25
49.99884
5
75
1575
900
1245
875
53165000
Universitas Sumatera Utara
Iterasi 13
Basis / C
s1
0
s2
0
s8
0
s4
0
s9
0
s6
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.2
-0.6
0.99998
-1
0
0.99998
0
0.99998
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
-0.2
0.05002
-0.75
0.75
1
-0.75
1
-0.75
1
0
0
250
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
-0.1
0.05002
-0.75
0.75
0
-0.75
0
-0.75
0
0
1
250
0
s8
1.20006
0.60001
1.00002
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
-0.2
0
1
-1
0
2
0
1
0
-1
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49989.5
9592.751
8.749969
16.25003
49.99884
13.74997
49.99884
1583.75
900
1245
875
53278750
Karena baris Zj - Cj ≥ 0, maka permasalahan telah optimal.
Berdasarkan perhitungan awal metode simpleks, diperoleh nilai x1 = 1583,75, x2 = 900, x3 = 1245, dan x4 = 875 dengan z = 53278750.
Universitas Sumatera Utara
Lampiran 2. Percabangan Metode Branch and Bound.
Iterasi 001
z = 53278750
x1=1583,75;x2=900;x3=1245;x4=875
x1≥1584
x1≤1583
Iterasi 002
z = 53278000
x1=1583;x2=900;x3=1245,75;x4=875
x3≥1246
x3≤1245
Iterasi 003
z = 53269000
x1=1583;x2=900;x3=1245;x4=875
Iterasi 004
z = 53277750
x1=1582,75;x2=900;x3=1246;x4=875
Iterasi 023
z = 53278670
x1=1584;x2=900;x3=1245;x4=874,67
Iterasi 024
z = 53278500
x1=1584,5;x2=900;x3=1245;x4=874
Iterasi 005
z = 53277000
x1=1582;x2=900;x3=1246,75;x4=875
Iterasi 006
z = 53268000
x1=1582;x2=900;x3=1246;x4=875
Iterasi 049
z = 53278670
x1=1584;x2=899,67;x3=1245;x4=875
x1≥1583
x1≤1582
x3≤1246
x4≥875
x4≤874
x3≥1247
Iterasi 007
z = 53276750
x1=1581,75;x2=900;x3=1247;x4=875
Iterasi 065
z = 53277670
x1=1583;x2=900;x3=1246;x4=874,67
x4≤874
Iterasi 066
z = 53277000
x1=1583;x2=900;x3=1246,5;x4=874
x4≥875
Iterasi 077
z = 53277670
x1=1583;x2=899,67;x3=1246;x4=875
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Iterasi 007
x1≥1582
x1≤1581
Iterasi 008
z = 53273000
x1=1581;x2=900;x3=1247,75;x4=875
x3≤1247
Iterasi 086
z = 53276670
x1=1582;x2=900;x3=1247;x4=874,67
x3≥1248
Iterasi 010
z = 53275750
x1=1580,75;x2=900;x3=1248;x4=875
Iterasi 009
z = 53267000
x1=1581;x2=900;x3=1247;x4=875
x1≤1580
x4≤874
Iterasi 087
z = 53276000
x1=1582;x2=900;x3=1247,5;x4=874
Iterasi 012
z = 53266000
x1=1580;x2=900;x3=1248;x4=875
Iterasi 097
z = 53276670
x1=1582;x2=899,67;x3=1247;x4=875
x1≥1581
Iterasi 011
z = 53275000
x1=1580;x2=900;x3=1248,75;x4=875
x3≤1248
x4≥875
Iterasi 106
z = 53275670
x1=1581;x2=900;x3=1248;x4=874,67
x3≥1249
x4≤874
x4≥875
Iterasi 013
z = 53274750
x1=1579,75;x2=900;x3=1249;x4=875
Iterasi 107
z = 53275000
x1=1581;x2=900;x3=1248,5;x4=874
Iterasi 118
z = 53275670
x1=1581;x2=899,67;x3=1248;x4=875
x1≤1579
Iterasi 014
z = 53274000
x1=1579;x2=900;x3=1249,75;x4=875
x1≥1580
Iterasi 127
z = 53274670
x1=1580;x2=900;x3=1249;x4=874,67
Universitas Sumatera Utara
Iterasi 014
x3≤1249
Iterasi 127
x3≥1250
Iterasi 015
z = 53265000
x1=1579;x2=900;x3=1249;x4=875
x4≤874
Iterasi 016
z = 53273750
x1=1578,75;x2=900;x3=1250;x4=875
x1≤1578
x4≥875
Iterasi 128
No Feasible Solution
Iterasi 129
No Feasible Solution
x1≥1579
Iterasi 017
z = 53264000
x1=1578;x2=900;x3=1250;x4=875
Iterasi 018
z = 53273670
x1=1579;x2=900;x3=1250;x4=874,67
x4≤ 874
x4≥ 875
Iterasi 019
z = 53267000
x1=1579;x2=900;x3=1250;x4=874
Iterasi 020
z = 53273670
x1=1579;x2=899,67;x3=1250;x4=875
x2 ≤ 899
Iterasi 021
z = 53267000
x1=1579;x2=899;x3=1250;x4=875
x2 ≥ 900
Iterasi 022
No Feasible Solution
Universitas Sumatera Utara
Iterasi 024
x1≤1584
x1≥1585
Iterasi 025
z = 53278000
x1=1584;x2=900;x3=1245,75;x4=874
x3≤1245
Iterasi 026
z = 53272000
x1=1584;x2=900;x3=1245;x4=874
Iterasi 036
z = 53278330
x1=1585;x2=900;x3=1245;x4=873,33
x3≥1246
x4≤874
Iterasi 027
z = 53277330
x1=1584;x2=900;x3=1246;x4=873,33
Iterasi 037
z = 53278250
x1=1585,25;x2=900;x3=1245;x4=873
x4≤873
Iterasi 029
z = 53274000
x1=1584;x2=900;x3=1246;x4=873
Iterasi 042
z = 53278330
x1=1585;x2=899,33;x3=1245;x4=874
x4≥874
Iterasi 028
z = 53277000
x1=1584;x2=900;x3=1246,25;x4=873
x3≤1246
x4≥875
Iterasi 031
z = 53277330
x1=1584;x2=899,33;x3=1246;x4=874
x3≥1247
x2≤899
Iterasi 030
z = 53276000
x1=1584;x2=900;x3=1247;x4=872
x2≥900
Iterasi 032
z = 53277000
x1=1584;x2=899;x3=1246,25;x4=874
x3≤1246
Iterasi 033
z = 53274000
x1=1584;x2=899;x3=1246;x4=874
Iterasi 035
No Feasible Solution
x3≥1247
Iterasi 034
z = 53276000
x1=1584;x2=898;x3=1247;x4=874
Universitas Sumatera Utara
Iterasi 037
x1≤1585
Iterasi 038
z = 53278000
x1=1585;x2=900;x3=1245,25;x4=873
x3≤1245
Iterasi 039
z = 53275000
x1=1585;x2=900;x3=1245;x4=873
Iterasi 042
x1≥1586
x4≤874
Iterasi 041
z = 53278000
x1=1586;x2=900;x3=1245;x4=872
x3≥1246
x4≥875
Iterasi 043
z = 53278250
x1=1585,25;x2=899;x3=1245;x4=874
x1≥1586
x1≤1585
Iterasi 040
z = 53277000
x1=1585;x2=900;x3=1246;x4=872
Iterasi 048
No Feasible Solution
Iterasi 044
z = 53278000
x1=1585;x2=899;x3=1245,25;x4=874
x3≤1245
Iterasi 047
z = 53278000
x1=1586;x2=898;x3=1245;x4=874
x3≥1246
Iterasi 045
z = 53275000
x1=1585;x2=899;x3=1245;x4=874
Iterasi 046
z = 53277000
x1=1585;x2=898;x3=1245;x4=874
Iterasi 049
x2≤899
Iterasi 050
z = 53278500
x1=1584,5;x2=899;x3=1245;x4=875
x2≥900
Iterasi 065
No Feasible Solution
Universitas Sumatera Utara
Iterasi 050
x1≤1584
x1≥1585
Iterasi 051
z = 53278000
x1=1584;x2=899;x3=1245,5;x4=875
x3≤1245
Iterasi 052
z = 53272000
x1=1584;x2=899;x3=1245;x4=875
Iterasi 058
z = 53278330
x1=1585;x2=898,33;x3=1245;x4=875
x3≥1246
Iterasi 053
z = 53277330
x1=1584;x2=898,33;x3=1246;x4=875
x2≥899
x2≤898
Iterasi 054
z = 53277000
x1=1584;x2=898;x3=1246,25;x4=875
x3≤1246
Iterasi 055
z = 53274000
x1=1584;x2=898;x3=1246;x4=875
Iterasi 057
No Feasible Solution
x3≥1247
Iterasi 056
z = 53276000
x1=1584;x2=897;x3=1247;x4=875
x2≤898
Iterasi 059
z = 53278250
x1=1585,25;x2=898;x3=1245;x4=875
x1≤1585
Iterasi 060
z = 53278000
x1=1585;x2=898;x3=1245,25;x4=875
x3≤1245
Iterasi 061
z = 53275000
x1=1585;x2=898;x3=1245;x4=875
x2≥899
Iterasi 064
No Feasible Solution
x1≥1586
Iterasi 063
z = 53278000
x1=1586;x2=897;x3=1245;x4=875
x3≥1246
Iterasi 062
z = 53277000
x1=1585;x2=897;x3=1246;x4=875
Universitas Sumatera Utara
Iterasi 066
x3≤1246
Iterasi 067
z = 53271000
x1=1583;x2=900;x3=1246;x4=874
x3≥1247
Iterasi 068
z = 53276330
x1=1583;x2=900;x3=1247;x4=873,33
x4≥874
x4≤873
Iterasi 069
z = 53276000
x1=1583;x2=900;x3=1247,25;x4=873
x3≤1247
Iterasi 070
z = 53273000
x1=1583;x2=900;x3=1247;x4=873
Iterasi 072
z = 53276330
x1=1583;x2=899,33;x3=1247;x4=874
x3≥1248
x2≥900
x2≤899
Iterasi 071
z = 53275000
x1=1583;x2=900;x3=1248;x4=872
Iterasi 073
z = 53276000
x1=1583;x2=899;x3=1247,25;x4=874
x3≤1247
Iterasi 074
z = 53273000
x1=1583;x2=899;x3=1247;x4=874
Iterasi 076
No Feasible Solution
x3≥1248
Iterasi 075
z = 53275000
x1=1583;x2=898;x3=1248;x4=874
Universitas Sumatera Utara
Iterasi 077
x2≤899
x2≥900
Iterasi 078
z = 53277000
x1=1583;x2=899;x3=1246,5;x4=875
x3≤1246
Iterasi 085
No Feasible Solution
x3≥1247
Iterasi 080
z = 53276330
x1=1583;x2=898,33;x3=1247;x4=875
Iterasi 079
z = 53271000
x1=1583;x2=899;x3=1246;x4=875
x2≤898
x2≥899
Iterasi 081
z = 53276000
x1=1583;x2=898;x3=1247,25;x4=875
Iterasi 084
No Feasible Solution
x3≤1247
Iterasi 082
z = 53273000
x1=1583;x2=898;x3=1247;x4=875
x3≥1248
Iterasi 083
z = 53275000
x1=1583;x2=897;x3=1248;x4=875
Universitas Sumatera Utara
Iterasi 087
x3≤1247
Iterasi 088
z = 53270000
x1=1582;x2=900;x3=1247;x4=874
x3≥1248
Iterasi 089
z = 53275330
x1=1582;x2=900;x3=1248;x4=873,33
x4≥874
x4≤873
Iterasi 090
z = 53275000
x1=1582;x2=900;x3=1248,25;x4=873
x3≤1248
Iterasi 091
z = 53272000
x1=1582;x2=900;x3=1248;x4=873
Iterasi 093
z = 53275330
x1=1582;x2=899,33;x3=1248;x4=874
x3≥1249
x2≥900
x2≤899
Iterasi 092
z = 53274000
x1=1582;x2=900;x3=1249;x4=872
Iterasi 094
z = 53275000
x1=1582;x2=899;x3=1248,25;x4=874
x3≤1248
Iterasi 095
z = 53272000
x1=1582;x2=899;x3=1248;x4=874
Iterasi 076
No Feasible Solution
x3≥1249
Iterasi 096
z = 53274000
x1=1582;x2=898;x3=1249;x4=874
Universitas Sumatera Utara
Iterasi 097
x2≤899
x2≥900
Iterasi 098
z = 53276000
x1=1582;x2=899;x3=1247,5;x4=875
x3≤1247
Iterasi 105
No Feasible Solution
x3≥1248
Iterasi 100
z = 53275330
x1=1582;x2=898,33;x3=1248;x4=875
Iterasi 099
z = 53270000
x1=1582;x2=899;x3=1247;x4=875
x2≤898
x2≥899
Iterasi 101
z = 53275000
x1=1582;x2=898;x3=1248,25;x4=875
Iterasi 104
No Feasible Solution
x3≤1248
Iterasi 102
z = 53272000
x1=1582;x2=898;x3=1248;x4=875
x3≥1249
Iterasi 103
z = 53271000
x1=1582;x2=897;x3=1249;x4=875
Universitas Sumatera Utara
Iterasi 107
x3≤1248
Iterasi 108
z = 53269000
x1=1581;x2=900;x3=1248;x4=874
x3≥1249
Iterasi 109
z = 53274330
x1=1581;x2=900;x3=1249;x4=873,33
x4≥874
x4≤873
Iterasi 110
z = 53274000
x1=1581;x2=900;x3=1249,25;x4=873
x3≤1249
Iterasi 111
z = 53271000
x1=1581;x2=900;x3=1249;x4=873
Iterasi 113
z = 53274330
x1=1581;x2=899,33;x3=1249;x4=874
x3≥1250
x2≥900
x2≤899
Iterasi 112
z = 53273000
x1=1581;x2=900;x3=1250;x4=872
Iterasi 114
z = 53274000
x1=1581;x2=899;x3=1249,25;x4=874
x3≤1249
Iterasi 115
z = 53271000
x1=1581;x2=899;x3=1249;x4=874
Iterasi 117
No Feasible Solution
x3≥1250
Iterasi 116
z = 53273000
x1=1581;x2=898;x3=1250;x4=874
Universitas Sumatera Utara
Iterasi 118
x2≤899
x2≥900
Iterasi 119
z = 53275000
x1=1581;x2=899;x3=1248,5;x4=875
x3≤1248
Iterasi 126
No Feasible Solution
x3≥1249
Iterasi 121
z = 53274330
x1=1581;x2=898,33;x3=1249;x4=875
Iterasi 120
z = 53269000
x1=1581;x2=899;x3=1248;x4=875
x2≤898
x2≥899
Iterasi 122
z = 53274000
x1=1581;x2=898;x3=1249,25;x4=875
Iterasi 125
No Feasible Solution
x3≤1249
Iterasi 123
z = 53271000
x1=1581;x2=898;x3=1249;x4=875
x3≥1250
Iterasi 124
z = 53270000
x1=1581;x2=897;x3=1250;x4=875
Universitas Sumatera Utara
Iterasi 0
Basis / C
s1
0
s2
0
s3
0
s4
0
s5
0
s6
0
s7
0
s12
M
s13
M
s14
M
s15
M
Zj - Cj
13000
x1
1.2
0.6
1
1
0
0
0
1
0
0
0
M-13000
10000
x2
1.1
0.4
0.75
0
1
0
0
0
1
0
0
M-10000
12000
x3
1
0.6
1
0
0
1
0
0
0
1
0
M-12000
10000
x4
1
0.4
0.75
0
0
0
1
0
0
0
1
M-10000
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
0
0
0
0
-1
0
0
0
-M
0
s9
0
0
0
0
0
0
0
0
-1
0
0
-M
0
s10
0
0
0
0
0
0
0
0
0
-1
0
-M
0
s11
0
0
0
0
0
0
0
0
0
0
-1
-M
M
s12
0
0
0
0
0
0
0
1
0
0
0
0
M
s13
0
0
0
0
0
0
0
0
1
0
0
0
M
s14
0
0
0
0
0
0
0
0
0
1
0
0
M
s15
0
0
0
0
0
0
0
0
0
0
1
0
Universitas Sumatera Utara
B
55000
12000
4160
1600
900
1250
875
1575
850
1245
800
4470M
Iterasi 1
13000
x1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13000
1
M
0
M
0
M
0
Basis / C
s1
s2
s3
s4
s5
s6
s7
x1
s13
s14
s15
Zj - Cj
0
10000
x2
1.1
0.4
0.75
0
1
0
0
0
1
0
0
12000
x3
1
0.6
1
0
0
1
0
0
0
1
0
10000
x4
1
0.4
0.75
0
0
0
1
0
0
0
1
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
0
s9
0
0
0
0
0
0
0
0
-1
0
0
0
s10
0
0
0
0
0
0
0
0
0
-1
0
0
s11
0
0
0
0
0
0
0
0
0
0
-1
M
s13
0
0
0
0
0
0
0
0
1
0
0
M
s14
0
0
0
0
0
0
0
0
0
1
0
M
s15
0
0
0
0
0
0
0
0
0
0
1
M-10000
M-12000
M-10000
0
0
0
0
0
0
0
-13000
-M
-M
-M
0
0
0
B
53110
11055
2585
25
900
1250
875
1575
850
1245
800
2895M+20475000
Universitas Sumatera Utara
Iterasi 2
13000
10000
12000
x1
x2
x3
s1
0
0
1.1
0
s2
0
0
0.4
0
s3
0
0
0.75
0
s4
0
0
0
0
s5
0
0
1
0
s6
0
0
0
0
s7
0
0
0
0
x1 13000
1
0
0
s13
M
0
1
0
x3 12000
0
0
1
s15
M
0
0
0
Zj - Cj
0
M-10000
0
Basis / C
10000
x4
1
0.4
0.75
0
0
0
1
0
0
0
1
M-10000
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
0
0
0
0
-1
0
0
-M
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
0
0
0
0
0
0
0
0
0
0
-1
-M
M
s13
0
0
0
0
0
0
0
0
1
0
0
0
M
s15
0
0
0
0
0
0
0
0
0
0
1
0
B
51865
10308
1340
25
900
5
875
1575
850
1245
800
1650M+35415000
Universitas Sumatera Utara
Iterasi 3
13000
10000
12000
x1
x2
x3
s1
0
0
1.1
0
s2
0
0
0.4
0
s3
0
0
0.75
0
s4
0
0
0
0
s5
0
0
1
0
s6
0
0
0
0
s7
0
0
0
0
x1 13000
1
0
0
s13
M
0
1
0
x3 12000
0
0
1
x4 10000
0
0
0
Zj - Cj
0
M-10000
0
Basis / C
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
0
0
0
0
-1
0
0
-M
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
M
s13
0
0
0
0
0
0
0
0
1
0
0
0
B
51065
9988
740
25
900
5
75
1575
850
1245
800
850M+43415000
Universitas Sumatera Utara
Iterasi 4
Basis / C
s1
s2
s3
s4
s5
s6
s7
x1
x2
x3
x4
0
0
0
0
0
0
0
13000
10000
12000
10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
1.2
0.6
1
1
0
0
0
-1
0
0
0
-13000
0
s9
1.1
0.4
0.75
0
1
0
0
0
-1
0
0
-10000
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50130
9648
102.5
25
50
5
75
1575
850
1245
800
51915000
Universitas Sumatera Utara
Iterasi 5
Basis / C
s1
s2
s3
s8
s5
s6
s7
x1
x2
x3
x4
0
0
0
0
0
0
0
13000
10000
12000
10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
-1.2
-0.6
-1
1
0
0
0
1
0
0
0
13000
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
1.1
0.4
0.75
0
1
0
0
0
-1
0
0
-10000
0
s10
1
0.6
1
0
0
1
0
0
0
-1
0
-12000
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50100
9633
77.5
25
50
5
75
1600
850
1245
800
52240000
Universitas Sumatera Utara
Iterasi 6
Basis / C
s1
0
s2
0
s3
0
s8
0
s5
0
s10
0
s7
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
-1.2
-0.6
-1
1
0
0
0
1
0
0
0
13000
0
s5
0
0
0
0
1
0
0
0
0
0
0
0
0
s6
-1
-0.6
-1
0
0
1
0
0
0
1
0
12000
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
1.1
0.4
0.75
0
1
0
0
0
-1
0
0
-10000
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50095
9630
72.5
25
50
5
75
1600
850
1250
800
52300000
Universitas Sumatera Utara
Iterasi 7
Basis / C
s1
0
s2
0
s3
0
s8
0
s9
0
s10
0
s7
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
s4
s5
s6
-1.2
-1.1
-1
-0.6
-0.4
-0.6
-1
-0.75
-1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
13000 10000 12000
0
s7
0
0
0
0
0
0
1
0
0
0
0
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
1
0.4
0.75
0
0
0
1
0
0
0
-1
-10000
B
50040
9610
35
25
50
5
75
1600
900
1250
800
52300000
Universitas Sumatera Utara
Iterasi 8
Basis / C
s1
0
s2
0
s3
0
s8
0
s9
0
s10
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
s4
s5
s6
s7
-1.2
-1.1
-1
-1
-0.6
-0.4
-0.6
-0.4
-1
-0.75
-1
-0.75
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
13000 10000 12000 10000
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49965
9580
-21.25
25
50
5
75
1600
900
1250
875
52300000
Universitas Sumatera Utara
Iterasi 9
Basis / C
s1
0
s2
0
s5
0
s8
0
s9
0
s10
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.4667
-0.5333
-1.3333
0
1.33333
0
0
0
1.33333
0
0
0
0
s4
0.26667
-0.0667
1.33333
1
-1.3333
0
0
1
-1.3333
0
0
-13333
0
s5
0
0
1
0
0
0
0
0
0
0
0
0
0
s6
0.46667
-0.0667
1.33333
0
-1.3333
1
0
0
-1.3333
1
0
-13333
0
s7
0.1
0
1
0
-1
0
1
0
-1
0
1
0
0
s8
0
0
0
1
0
0
0
0
0
0
0
0
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49996.17
9591.333
28.33333
25
21.66667
5
75
1600
871.6667
1250
875
53266667
Universitas Sumatera Utara
Iterasi 10
Basis / C
s1
0
s2
0
s5
0
s4
0
s9
0
s10
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.4667
-0.5333
-1.3333
0
1.33333
0
0
0
1.33333
0
0
13333
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
1
0
0
0
0
0
0
0
0
0
0
s6
0.46667
-0.0667
1.33333
0
-1.3333
1
0
0
-1.3333
1
0
-13333
0
s7
0.1
0
1
0
-1
0
1
0
-1
0
1
0
0
s8
-0.2667
0.0667
-1.3333
1
1.3333
0
0
-1
1.3333
0
0
333
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
0
0
0
0
0
1
0
0
0
0
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49989.5
9593.001
-4.99992
25
54.99917
5
75
1575
904.9992
1250
875
53274992
Universitas Sumatera Utara
Iterasi 11
Basis / C
s1
0
s2
0
s5
0
s4
0
s9
0
s6
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.4667
-0.5333
-1.3333
0
1.33333
0
0
0
1.33333
0
0
13333
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
0
0
1
0
0
0
0
0
0
0
0
0
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
0.1
0
1
0
-1
0
1
0
-1
0
1
0
0
s8
-0.2667
0.0667
-1.3333
1
1.3333
0
0
-1
1.3333
0
0
333
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
-0.4667
0.0667
-1.3333
0
1.3333
1
0
0
1.3333
-1
0
1333
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49987.17
9593.334
-11.6666
25
61.66567
5
75
1575
911.6657
1245
875
53281657
Universitas Sumatera Utara
Iterasi 12
Basis / C
s1
0
s2
0
s3
0
s4
0
s9
0
s6
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
0
0
1
0
0
0
0
0
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
-1.1001
-0.4
-0.75
0
1
0
0
0
1
0
0
10000
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
-1.0001
-0.4
-0.75
0
0
0
1
0
0
0
1
10000
0
s8
1.20006
0.60001
1.00002
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
1.00006
0.60001
1.00002
0
0
1
0
0
0
-1
0
-12000
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
50000
9598.001
8.750144
25
49.99884
5
75
1575
900
1245
875
53165000
Universitas Sumatera Utara
Iterasi 13
Basis / C
s1
0
s2
0
s8
0
s4
0
s9
0
s6
0
s11
0
x1 13000
x2 10000
x3 12000
x4 10000
Zj - Cj
13000
x1
0
0
0
0
0
0
0
1
0
0
0
0
10000
x2
0
0
0
0
0
0
0
0
1
0
0
0
12000
x3
0
0
0
0
0
0
0
0
0
1
0
0
10000
x4
0
0
0
0
0
0
0
0
0
0
1
0
0
s1
1
0
0
0
0
0
0
0
0
0
0
0
0
s2
0
1
0
0
0
0
0
0
0
0
0
0
0
s3
-1.2
-0.6
0.99998
-1
0
0.99998
0
0.99998
0
0
0
0
0
s4
0
0
0
1
0
0
0
0
0
0
0
0
0
s5
-0.2
0.05002
-0.75
0.75
1
-0.75
1
-0.75
1
0
0
250
0
s6
0
0
0
0
0
1
0
0
0
0
0
0
0
s7
-0.1
0.05002
-0.75
0.75
0
-0.75
0
-0.75
0
0
1
250
0
s8
1.20006
0.60001
1.00002
1
0
0
0
-1
0
0
0
-13000
0
s9
0
0
0
0
1
0
0
0
0
0
0
0
0
s10
-0.2
0
1
-1
0
2
0
1
0
-1
0
0
0
s11
0
0
0
0
0
0
1
0
0
0
0
0
B
49989.5
9592.751
8.749969
16.25003
49.99884
13.74997
49.99884
1583.75
900
1245
875
53278750
Karena baris Zj - Cj ≥ 0, maka permasalahan telah optimal.
Berdasarkan perhitungan awal metode simpleks, diperoleh nilai x1 = 1583,75, x2 = 900, x3 = 1245, dan x4 = 875 dengan z = 53278750.
Universitas Sumatera Utara
Lampiran 2. Percabangan Metode Branch and Bound.
Iterasi 001
z = 53278750
x1=1583,75;x2=900;x3=1245;x4=875
x1≥1584
x1≤1583
Iterasi 002
z = 53278000
x1=1583;x2=900;x3=1245,75;x4=875
x3≥1246
x3≤1245
Iterasi 003
z = 53269000
x1=1583;x2=900;x3=1245;x4=875
Iterasi 004
z = 53277750
x1=1582,75;x2=900;x3=1246;x4=875
Iterasi 023
z = 53278670
x1=1584;x2=900;x3=1245;x4=874,67
Iterasi 024
z = 53278500
x1=1584,5;x2=900;x3=1245;x4=874
Iterasi 005
z = 53277000
x1=1582;x2=900;x3=1246,75;x4=875
Iterasi 006
z = 53268000
x1=1582;x2=900;x3=1246;x4=875
Iterasi 049
z = 53278670
x1=1584;x2=899,67;x3=1245;x4=875
x1≥1583
x1≤1582
x3≤1246
x4≥875
x4≤874
x3≥1247
Iterasi 007
z = 53276750
x1=1581,75;x2=900;x3=1247;x4=875
Iterasi 065
z = 53277670
x1=1583;x2=900;x3=1246;x4=874,67
x4≤874
Iterasi 066
z = 53277000
x1=1583;x2=900;x3=1246,5;x4=874
x4≥875
Iterasi 077
z = 53277670
x1=1583;x2=899,67;x3=1246;x4=875
Universitas Sumatera Utara
Iterasi 007
x1≥1582
x1≤1581
Iterasi 008
z = 53273000
x1=1581;x2=900;x3=1247,75;x4=875
x3≤1247
Iterasi 086
z = 53276670
x1=1582;x2=900;x3=1247;x4=874,67
x3≥1248
Iterasi 010
z = 53275750
x1=1580,75;x2=900;x3=1248;x4=875
Iterasi 009
z = 53267000
x1=1581;x2=900;x3=1247;x4=875
x1≤1580
x4≤874
Iterasi 087
z = 53276000
x1=1582;x2=900;x3=1247,5;x4=874
Iterasi 012
z = 53266000
x1=1580;x2=900;x3=1248;x4=875
Iterasi 097
z = 53276670
x1=1582;x2=899,67;x3=1247;x4=875
x1≥1581
Iterasi 011
z = 53275000
x1=1580;x2=900;x3=1248,75;x4=875
x3≤1248
x4≥875
Iterasi 106
z = 53275670
x1=1581;x2=900;x3=1248;x4=874,67
x3≥1249
x4≤874
x4≥875
Iterasi 013
z = 53274750
x1=1579,75;x2=900;x3=1249;x4=875
Iterasi 107
z = 53275000
x1=1581;x2=900;x3=1248,5;x4=874
Iterasi 118
z = 53275670
x1=1581;x2=899,67;x3=1248;x4=875
x1≤1579
Iterasi 014
z = 53274000
x1=1579;x2=900;x3=1249,75;x4=875
x1≥1580
Iterasi 127
z = 53274670
x1=1580;x2=900;x3=1249;x4=874,67
Universitas Sumatera Utara
Iterasi 014
x3≤1249
Iterasi 127
x3≥1250
Iterasi 015
z = 53265000
x1=1579;x2=900;x3=1249;x4=875
x4≤874
Iterasi 016
z = 53273750
x1=1578,75;x2=900;x3=1250;x4=875
x1≤1578
x4≥875
Iterasi 128
No Feasible Solution
Iterasi 129
No Feasible Solution
x1≥1579
Iterasi 017
z = 53264000
x1=1578;x2=900;x3=1250;x4=875
Iterasi 018
z = 53273670
x1=1579;x2=900;x3=1250;x4=874,67
x4≤ 874
x4≥ 875
Iterasi 019
z = 53267000
x1=1579;x2=900;x3=1250;x4=874
Iterasi 020
z = 53273670
x1=1579;x2=899,67;x3=1250;x4=875
x2 ≤ 899
Iterasi 021
z = 53267000
x1=1579;x2=899;x3=1250;x4=875
x2 ≥ 900
Iterasi 022
No Feasible Solution
Universitas Sumatera Utara
Iterasi 024
x1≤1584
x1≥1585
Iterasi 025
z = 53278000
x1=1584;x2=900;x3=1245,75;x4=874
x3≤1245
Iterasi 026
z = 53272000
x1=1584;x2=900;x3=1245;x4=874
Iterasi 036
z = 53278330
x1=1585;x2=900;x3=1245;x4=873,33
x3≥1246
x4≤874
Iterasi 027
z = 53277330
x1=1584;x2=900;x3=1246;x4=873,33
Iterasi 037
z = 53278250
x1=1585,25;x2=900;x3=1245;x4=873
x4≤873
Iterasi 029
z = 53274000
x1=1584;x2=900;x3=1246;x4=873
Iterasi 042
z = 53278330
x1=1585;x2=899,33;x3=1245;x4=874
x4≥874
Iterasi 028
z = 53277000
x1=1584;x2=900;x3=1246,25;x4=873
x3≤1246
x4≥875
Iterasi 031
z = 53277330
x1=1584;x2=899,33;x3=1246;x4=874
x3≥1247
x2≤899
Iterasi 030
z = 53276000
x1=1584;x2=900;x3=1247;x4=872
x2≥900
Iterasi 032
z = 53277000
x1=1584;x2=899;x3=1246,25;x4=874
x3≤1246
Iterasi 033
z = 53274000
x1=1584;x2=899;x3=1246;x4=874
Iterasi 035
No Feasible Solution
x3≥1247
Iterasi 034
z = 53276000
x1=1584;x2=898;x3=1247;x4=874
Universitas Sumatera Utara
Iterasi 037
x1≤1585
Iterasi 038
z = 53278000
x1=1585;x2=900;x3=1245,25;x4=873
x3≤1245
Iterasi 039
z = 53275000
x1=1585;x2=900;x3=1245;x4=873
Iterasi 042
x1≥1586
x4≤874
Iterasi 041
z = 53278000
x1=1586;x2=900;x3=1245;x4=872
x3≥1246
x4≥875
Iterasi 043
z = 53278250
x1=1585,25;x2=899;x3=1245;x4=874
x1≥1586
x1≤1585
Iterasi 040
z = 53277000
x1=1585;x2=900;x3=1246;x4=872
Iterasi 048
No Feasible Solution
Iterasi 044
z = 53278000
x1=1585;x2=899;x3=1245,25;x4=874
x3≤1245
Iterasi 047
z = 53278000
x1=1586;x2=898;x3=1245;x4=874
x3≥1246
Iterasi 045
z = 53275000
x1=1585;x2=899;x3=1245;x4=874
Iterasi 046
z = 53277000
x1=1585;x2=898;x3=1245;x4=874
Iterasi 049
x2≤899
Iterasi 050
z = 53278500
x1=1584,5;x2=899;x3=1245;x4=875
x2≥900
Iterasi 065
No Feasible Solution
Universitas Sumatera Utara
Iterasi 050
x1≤1584
x1≥1585
Iterasi 051
z = 53278000
x1=1584;x2=899;x3=1245,5;x4=875
x3≤1245
Iterasi 052
z = 53272000
x1=1584;x2=899;x3=1245;x4=875
Iterasi 058
z = 53278330
x1=1585;x2=898,33;x3=1245;x4=875
x3≥1246
Iterasi 053
z = 53277330
x1=1584;x2=898,33;x3=1246;x4=875
x2≥899
x2≤898
Iterasi 054
z = 53277000
x1=1584;x2=898;x3=1246,25;x4=875
x3≤1246
Iterasi 055
z = 53274000
x1=1584;x2=898;x3=1246;x4=875
Iterasi 057
No Feasible Solution
x3≥1247
Iterasi 056
z = 53276000
x1=1584;x2=897;x3=1247;x4=875
x2≤898
Iterasi 059
z = 53278250
x1=1585,25;x2=898;x3=1245;x4=875
x1≤1585
Iterasi 060
z = 53278000
x1=1585;x2=898;x3=1245,25;x4=875
x3≤1245
Iterasi 061
z = 53275000
x1=1585;x2=898;x3=1245;x4=875
x2≥899
Iterasi 064
No Feasible Solution
x1≥1586
Iterasi 063
z = 53278000
x1=1586;x2=897;x3=1245;x4=875
x3≥1246
Iterasi 062
z = 53277000
x1=1585;x2=897;x3=1246;x4=875
Universitas Sumatera Utara
Iterasi 066
x3≤1246
Iterasi 067
z = 53271000
x1=1583;x2=900;x3=1246;x4=874
x3≥1247
Iterasi 068
z = 53276330
x1=1583;x2=900;x3=1247;x4=873,33
x4≥874
x4≤873
Iterasi 069
z = 53276000
x1=1583;x2=900;x3=1247,25;x4=873
x3≤1247
Iterasi 070
z = 53273000
x1=1583;x2=900;x3=1247;x4=873
Iterasi 072
z = 53276330
x1=1583;x2=899,33;x3=1247;x4=874
x3≥1248
x2≥900
x2≤899
Iterasi 071
z = 53275000
x1=1583;x2=900;x3=1248;x4=872
Iterasi 073
z = 53276000
x1=1583;x2=899;x3=1247,25;x4=874
x3≤1247
Iterasi 074
z = 53273000
x1=1583;x2=899;x3=1247;x4=874
Iterasi 076
No Feasible Solution
x3≥1248
Iterasi 075
z = 53275000
x1=1583;x2=898;x3=1248;x4=874
Universitas Sumatera Utara
Iterasi 077
x2≤899
x2≥900
Iterasi 078
z = 53277000
x1=1583;x2=899;x3=1246,5;x4=875
x3≤1246
Iterasi 085
No Feasible Solution
x3≥1247
Iterasi 080
z = 53276330
x1=1583;x2=898,33;x3=1247;x4=875
Iterasi 079
z = 53271000
x1=1583;x2=899;x3=1246;x4=875
x2≤898
x2≥899
Iterasi 081
z = 53276000
x1=1583;x2=898;x3=1247,25;x4=875
Iterasi 084
No Feasible Solution
x3≤1247
Iterasi 082
z = 53273000
x1=1583;x2=898;x3=1247;x4=875
x3≥1248
Iterasi 083
z = 53275000
x1=1583;x2=897;x3=1248;x4=875
Universitas Sumatera Utara
Iterasi 087
x3≤1247
Iterasi 088
z = 53270000
x1=1582;x2=900;x3=1247;x4=874
x3≥1248
Iterasi 089
z = 53275330
x1=1582;x2=900;x3=1248;x4=873,33
x4≥874
x4≤873
Iterasi 090
z = 53275000
x1=1582;x2=900;x3=1248,25;x4=873
x3≤1248
Iterasi 091
z = 53272000
x1=1582;x2=900;x3=1248;x4=873
Iterasi 093
z = 53275330
x1=1582;x2=899,33;x3=1248;x4=874
x3≥1249
x2≥900
x2≤899
Iterasi 092
z = 53274000
x1=1582;x2=900;x3=1249;x4=872
Iterasi 094
z = 53275000
x1=1582;x2=899;x3=1248,25;x4=874
x3≤1248
Iterasi 095
z = 53272000
x1=1582;x2=899;x3=1248;x4=874
Iterasi 076
No Feasible Solution
x3≥1249
Iterasi 096
z = 53274000
x1=1582;x2=898;x3=1249;x4=874
Universitas Sumatera Utara
Iterasi 097
x2≤899
x2≥900
Iterasi 098
z = 53276000
x1=1582;x2=899;x3=1247,5;x4=875
x3≤1247
Iterasi 105
No Feasible Solution
x3≥1248
Iterasi 100
z = 53275330
x1=1582;x2=898,33;x3=1248;x4=875
Iterasi 099
z = 53270000
x1=1582;x2=899;x3=1247;x4=875
x2≤898
x2≥899
Iterasi 101
z = 53275000
x1=1582;x2=898;x3=1248,25;x4=875
Iterasi 104
No Feasible Solution
x3≤1248
Iterasi 102
z = 53272000
x1=1582;x2=898;x3=1248;x4=875
x3≥1249
Iterasi 103
z = 53271000
x1=1582;x2=897;x3=1249;x4=875
Universitas Sumatera Utara
Iterasi 107
x3≤1248
Iterasi 108
z = 53269000
x1=1581;x2=900;x3=1248;x4=874
x3≥1249
Iterasi 109
z = 53274330
x1=1581;x2=900;x3=1249;x4=873,33
x4≥874
x4≤873
Iterasi 110
z = 53274000
x1=1581;x2=900;x3=1249,25;x4=873
x3≤1249
Iterasi 111
z = 53271000
x1=1581;x2=900;x3=1249;x4=873
Iterasi 113
z = 53274330
x1=1581;x2=899,33;x3=1249;x4=874
x3≥1250
x2≥900
x2≤899
Iterasi 112
z = 53273000
x1=1581;x2=900;x3=1250;x4=872
Iterasi 114
z = 53274000
x1=1581;x2=899;x3=1249,25;x4=874
x3≤1249
Iterasi 115
z = 53271000
x1=1581;x2=899;x3=1249;x4=874
Iterasi 117
No Feasible Solution
x3≥1250
Iterasi 116
z = 53273000
x1=1581;x2=898;x3=1250;x4=874
Universitas Sumatera Utara
Iterasi 118
x2≤899
x2≥900
Iterasi 119
z = 53275000
x1=1581;x2=899;x3=1248,5;x4=875
x3≤1248
Iterasi 126
No Feasible Solution
x3≥1249
Iterasi 121
z = 53274330
x1=1581;x2=898,33;x3=1249;x4=875
Iterasi 120
z = 53269000
x1=1581;x2=899;x3=1248;x4=875
x2≤898
x2≥899
Iterasi 122
z = 53274000
x1=1581;x2=898;x3=1249,25;x4=875
Iterasi 125
No Feasible Solution
x3≤1249
Iterasi 123
z = 53271000
x1=1581;x2=898;x3=1249;x4=875
x3≥1250
Iterasi 124
z = 53270000
x1=1581;x2=897;x3=1250;x4=875
Universitas Sumatera Utara