Minimizar z(x) = 4 x1 Sujeto a 3 x1 4 x1 x1 x1 + x2 + x2 + 3 x2 + 2 x2 x2 = ≥ ≤ ≥ 3 6 4 0 Forma standard Minimizar z(x) = 4 x1 Sujeto a 3 x1 4 x1 x1 x1 + x2 + x2 + a1 + 3 x 2 – s2 + + 2 x2 + s3 x2 s2 s3 a 1 a2 a2 = = = ≥ 3 6 4 0 = = = ≥ 3 6 4 0 Fase I a1 + a 2 Minimizar w(a) = Sujeto a 3 x1 + x2 + a1 4 x 1 + 3 x 2 – s2 + x 1 + 2 x2 + s3 x2 s2 s3 a 1 x1 a2 a2 Método Simplex Fase I F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 a1 a2 s3 -w -w′ -w′′ x1 3 4 1 0 -3 -7 x2 1 3 2 0 -1 -4 s2 0 -1 0 0 0 1 s3 0 0 1 0 0 0 a1 1 0 0 1 0 0 a2 0 1 0 1 1 0 b 3 6 4 0 -3 -9 x1 a2 s3 -w x1 1 0 0 0 x2 1/3 5/3 5/3 -5/3 s2 0 -1 0 1 s3 0 0 1 0 a1 1/3 -4/3 -1/3 7/3 a2 0 1 0 0 b 1 2 3 -2 x1 x2 s3 -w x1 1 0 0 0 x2 0 1 0 0 s2 1/5 -3/5 1 0 s3 0 0 1 0 a1 3/5 -4/5 1 1 a2 -1/5 3/5 -1 1 b 3/5 6/5 1 0 F4-F1 F5-F2 F1/3 F2-4F7 F3-F7 F6+7F7 F7-F12/3 F8/(5/3) F9-(5/3)F12 F10+(5/3)F12 Método Simplex Fase II F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 x1 x2 s3 -z -z′ -z′′ x1 1 0 0 4 0 0 x2 0 1 0 1 1 0 s2 1/5 -3/5 1 0 -4/5 -1/5 s3 0 0 1 0 0 0 b 3/5 6/5 1 0 -12/5 -18/5 x1 x2 s2 -z x1 1 0 0 0 x2 0 1 0 0 s2 0 0 1 0 s3 -1/5 3/5 1 1/5 b 2/5 9/5 1 -17/5 Solución óptima: x1 = 2/5 x2 = 9/5 s2 = 1 z* = 17/5 F4-4F1 F5-F2 F1-F9/5 F2+(3/5)F9 F6+F9/5