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

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

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

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

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

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

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

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

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

Tabel 2: CB Cj Basis 2 3 0 0 x1 x2 x3 x4 Const 3 x3 x2 –2 0 1 1 2 3 0 0 x1 x2 x3 x4 Const 3 x3 x2 –2 0 1 1 –3 1 0 1 6 4 ĈRow 11 0 0 –3 Z =12 yusuf fuad

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