Programaç˜ao Linear - Notas de aula - CEUNES

CAPÍTULO 8. MÉTODO SIMPLEX: INICIALIZAÇÃO E CICLAGEM 90Exemplo 8.3.1. [1] Considere o PL na forma padrãomin −x 1 +2x 2 −3x 3s.a. x 1 +x 2 +x 3 = 6−x 1 +x 2 +2x 3 = 42x 2 +3x 3 = 10x 3 +x 4 = 2x 1 , x 2 , x 3 , x 4 ≥ 0Introduzimos as variáveis artificiais x 5 , x 6 e x 7 :min −x 1 +2x 2 −3x 3s.a. x 1 +x 2 +x 3 +x 5 = 6−x 1 +x 2 +2x 3 +x 6 = 42x 2 +3x 3 +x 7 = 10x 3 +x 4 = 2x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 ≥ 0O QS inicial éz 0 x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 RHSz 1 0 1 −2 3 0 0 0 0 0x 0 0 1 0 4 6 0 0 0 0 20x 5 0 0 1 1 1 0 1 0 0 6x 6 0 0 −1 1 2 0 0 1 0 4x 7 0 0 0 2 3 0 0 0 1 10x 4 0 0 0 0 1 1 0 0 0 2z 0 x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 RHSz 1 0 1 −2 0 −3 0 0 0 −6x 0 0 1 0 4 0 −6 0 0 0 8x 5 0 0 1 1 0 −1 1 0 0 4x 6 0 0 −1 1 0 −2 0 1 0 0x 7 0 0 0 2 0 −3 0 0 1 4x 3 0 0 0 0 1 1 0 0 0 2z 0 x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 RHSz 1 0 −1 0 0 −7 0 2 0 −6x 0 0 1 4 0 0 2 0 −4 0 8x 5 0 0 2 0 0 1 1 −1 0 4x 2 0 0 −1 1 0 −2 0 1 0 0x 7 0 0 2 0 0 1 0 −2 1 4x 3 0 0 0 0 1 1 0 0 0 2z 0 x 0 x 1 x 2 x 3 x 4 x 5 x 6 x 7 RHSz 1 0 0 0 0 −13/2 −1/2 3/2 0 −4x 0 0 1 0 0 0 0 −2 −2 0 0x 1 0 0 1 0 0 1/2 1/2 −1/2 0 2x 2 0 0 0 1 0 −3/2 1/2 1/2 0 2x 7 0 0 0 0 0 0 −1 −1 1 0x 3 0 0 0 0 1 1 0 0 0 2