Ilustrasi-2 Maximize Z = 3x1 + 2x2 Subject to – x1 + 2x2 ≤ 4

Presentasi berjudul: "Ilustrasi-2 Maximize Z = 3x1 + 2x2 Subject to – x1 + 2x2 ≤ 4"— Transcript presentasi:

1 Ilustrasi-2 Maximize Z = 3x1 + 2x2 Subject to – x1 + 2x2 ≤ 4
yusuf fuad

2 In a standard form: Maximize Z = 3x1 + 2x2 Subject to
– x1 + 2x2 + x = 4 3x1 + 2x x = 14 x1 – x x5 = 3 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0, x5 ≥ 0 yusuf fuad

3 Tabel 1 CB Cj Basis 3 2 0 0 0 x1 x2 x3 x4 x5 Const x3 x4 x5 –1 2 1 0 0
x1 x2 x x4 x5 Const x3 x4 x5 – 1 – 4 14 3 ĈRow Z = 0 yusuf fuad

4 Tabel 2 CB Cj Basis 3 2 0 0 0 x1 x2 x3 x4 x5 Const 3 x3 x4 x1
x1 x2 x x4 x5 Const 3 x3 x4 x1 –3 1 – 7 5 ĈRow –3 Z = 9 yusuf fuad

5 Tabel 3 CB Cj Basis 3 2 0 0 0 x1 x2 x3 x4 x5 Const 2 3 x3 x2 x1
x1 x2 x x4 x5 Const 2 3 x3 x2 x1 –1/5 8/5 /5 –3/5 /5 2/5 6 1 4 ĈRow – Z = 14 yusuf fuad

6 Tabel 3 (alternative) CB Cj Basis 3 2 0 0 0 x1 x2 x3 x4 x5 Const 2 3
x1 x2 x x4 x5 Const 2 3 x5 x2 x1 /8 –1/8 1 /8 1/ –2/8 2/8 0 15/4 13/4 5/2 ĈRow – Z = 14 yusuf fuad

7 Solusi optimal tidak selalu tunggal
Beberapa kasus mungkin mempunyai solusi tunggal, mempunyai solusi tidak tunggal, tidak mempunyai solusi. yusuf fuad

8 Illustrasi-3 Maximize Z = 2x1 + 3x2 Subject to x1 – x2 ≤ 2
–3x1 + x2 ≤ 4 , x1 ≥ 0, x2 ≥ 0 Standard form x1 – x2 + x = 2 –3x1 + x x4 = 4 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0 yusuf fuad

9 Tabel 1: CB Cj Basis 2 3 0 0 x1 x2 x3 x4 Const x3 x4 1 –1 1 0 –3 1 0 1
x x x x4 Const x3 x4 1 – – 2 4 ĈRow Z =0 yusuf fuad

10 Tabel 2: CB Cj Basis 2 3 0 0 x1 x2 x3 x4 Const 3 x3 x2 –2 0 1 1
x x x x4 Const 3 x3 x2 – – 6 4 ĈRow –3 Z =12 yusuf fuad

11 Mengapa ilustrasi-3 tidak bisa dilanjutkan?
Apakah ada solusi optimalnya? yusuf fuad