\(maximize \; 40x1 + 35x2\) \(x1 + x2 \leq 24\) \(3x1 + 2x2 \leq 60\) \(x1,x2 \geq 0\)
Problema na forma padrão:
\(maximize \; 40x1 + 35x2 + 0x3 + 0x4\) \(x1 + x2 + 1x3 + 0x4 = 24\) \(3x1 + 2x2 + 0x3 + 1x4 = 60\) \(x1,x2,x3,x4 \geq 0\)
Ponto A: x1=0 x2=0 x3=24 x4=35
| L | VB | x1 | x2 | x3 | x4 | * |
|---|---|---|---|---|---|---|
| L1 | x3 | 1 | 1 | 1 | 0 | 24 |
| L2 | x4 | 3 | 2 | 0 | 1 | 60 |
| L3 | * | 40 | 35 | 0 | 0 | z |
x1 entra na base, x4 sai da base (60/3=20 < 24/1=24)
\(L1 \leftarrow L1 -1/3 L2\) \(L3 \leftarrow L3 -40/3 L2\) \(L2 \leftarrow L2/3\)
Ponto B: x1=20 x2=0 x3=4 x4=20
| L | VB | x1 | x2 | x3 | x4 | * |
|---|---|---|---|---|---|---|
| L1 | x3 | 0 | 1/3 | 1 | -1/3 | 4 |
| L2 | x1 | 1 | 2/3 | 0 | 1/3 | 20 |
| L3 | * | 0 | 25/3 | 0 | -40/3 | z - 800 |
x2 entra na base, x3 sai da base (4/(1/3)=12 < 24/1=24)
\(L2 \leftarrow L2 -2 L1\) \(L3 \leftarrow L3 -25 L1\) \(L2 \leftarrow L2/(1/3)\)
Ponto C: x1=12 x2=12 x3=0 x4=0
| L | VB | x1 | x2 | x3 | x4 | * |
|---|---|---|---|---|---|---|
| L1 | x2 | 0 | 1 | 3 | -1 | 12 |
| L2 | x1 | 1 | 0 | -2 | -1 | 12 |
| L3 | * | 0 | 0 | -25 | -15/3 | z - 900 |
Solução ótima! $z^* = 900$.