Simplex v3

Fonction objectif

Saisie : max(4x1+3x2+6x3)

Type : MAX

Methode : Deux phases

x1+x2+x3<=30
2x1+x2+3x3>=40
x1+2x2+x3=36
x1>=0
x2>=0
x3>=0

Entrante : x3 | Sortante : a1 | Pivot : L2, C3

Le plus petit rapport positif est : 40/3 sur la ligne a1 pour la colonne x3.

Base	x1 : 4	x2 : 3	x3 : 6	s1 : 0	s2 : 0	a1 : 0	a2 : 0	CST
s1 : 0	1	1	1	1	0	0	0	30(Rp : 30 / 1 = 30)
a1 : 0	2	1	3	0	-1	1	0	40(Rp : 40 / 3 = 13.33)
a2 : 0	1	2	1	0	0	0	1	36(Rp : 36 / 1 = 36)
Z	-3	-3	-4	0	1	0	0	-76

Entrante : x2 | Sortante : a2 | Pivot : L3, C2

Le plus petit rapport positif est : 68/5 sur la ligne a2 pour la colonne x2.

Base	x1 : 4	x2 : 3	x3 : 6	s1 : 0	s2 : 0	a1 : 0	a2 : 0	CST
s1 : 0	(1)-((1)*(2)/(3)) = 0.33	(1)-((1)*(1)/(3)) = 0.67	(1)-((1)*(3)/(3)) = 0	(1)-((1)*(0)/(3)) = 1	(0)-((1)*(-1)/(3)) = 0.33	(0)-((1)*(1)/(3)) = -0.33	(0)-((1)*(0)/(3)) = 0	(30)-((1)*(40)/(3)) = 16.67(Rp : 16.67 / 0.67 = 25)
x3 : 6	(2)/(3) = 0.67	(1)/(3) = 0.33	(3)/(3) = 1	(0)/(3) = 0	(-1)/(3) = -0.33	(1)/(3) = 0.33	(0)/(3) = 0	(40)/(3) = 13.33(Rp : 13.33 / 0.33 = 40)
a2 : 0	(1)-((1)*(2)/(3)) = 0.33	(2)-((1)*(1)/(3)) = 1.67	(1)-((1)*(3)/(3)) = 0	(0)-((1)*(0)/(3)) = 0	(0)-((1)*(-1)/(3)) = 0.33	(0)-((1)*(1)/(3)) = -0.33	(1)-((1)*(0)/(3)) = 1	(36)-((1)*(40)/(3)) = 22.67(Rp : 22.67 / 1.67 = 13.6)
Z	((01/3)+(02/3)+(-1*1/3))-(0) = -0.33	((02/3)+(01/3)+(-1*5/3))-(0) = -1.67	((00)+(01)+(-1*0))-(0) = 0	((01)+(00)+(-1*0))-(0) = 0	((01/3)+(0-1/3)+(-1*1/3))-(0) = -0.33	((0-1/3)+(01/3)+(-1*-1/3))-(-1) = 1.33	((00)+(00)+(-1*1))-(-1) = 0	(050/3)+(040/3)+(-1*68/3) = -22.67

Entrante : - | Sortante : - | Pivot : -

Base	x1 : 4	x2 : 3	x3 : 6	s1 : 0	s2 : 0	a1 : 0	a2 : 0	CST
s1 : 0	(1/3)-((2/3)*(1/3)/(5/3)) = 0.2	(2/3)-((2/3)*(5/3)/(5/3)) = 0	(0)-((2/3)*(0)/(5/3)) = 0	(1)-((2/3)*(0)/(5/3)) = 1	(1/3)-((2/3)*(1/3)/(5/3)) = 0.2	(-1/3)-((2/3)*(-1/3)/(5/3)) = -0.2	(0)-((2/3)*(1)/(5/3)) = -0.4	(50/3)-((2/3)*(68/3)/(5/3)) = 7.6
x3 : 6	(2/3)-((1/3)*(1/3)/(5/3)) = 0.6	(1/3)-((1/3)*(5/3)/(5/3)) = 0	(1)-((1/3)*(0)/(5/3)) = 1	(0)-((1/3)*(0)/(5/3)) = 0	(-1/3)-((1/3)*(1/3)/(5/3)) = -0.4	(1/3)-((1/3)*(-1/3)/(5/3)) = 0.4	(0)-((1/3)*(1)/(5/3)) = -0.2	(40/3)-((1/3)*(68/3)/(5/3)) = 8.8
x2 : 3	(1/3)/(5/3) = 0.2	(5/3)/(5/3) = 1	(0)/(5/3) = 0	(0)/(5/3) = 0	(1/3)/(5/3) = 0.2	(-1/3)/(5/3) = -0.2	(1)/(5/3) = 0.6	(68/3)/(5/3) = 13.6
Z	((01/5)+(03/5)+(0*1/5))-(0) = 0	((00)+(00)+(0*1))-(0) = 0	((00)+(01)+(0*0))-(0) = 0	((01)+(00)+(0*0))-(0) = 0	((01/5)+(0-2/5)+(0*1/5))-(0) = 0	((0-1/5)+(02/5)+(0*-1/5))-(-1) = 1	((0-2/5)+(0-1/5)+(0*3/5))-(-1) = 1	(038/5)+(044/5)+(0*68/5) = 0

Entrante : s2 | Sortante : s1 | Pivot : L1, C5

Le plus petit rapport positif est : 38 sur la ligne s1 pour la colonne s2.

Base	x1 : 4	x2 : 3	x3 : 6	s1 : 0	s2 : 0	CST
s1 : 0	0.2	0	0	1	0.2	7.6(Rp : 7.6 / 0.2 = 38)
x3 : 6	0.6	0	1	0	-0.4	8.8
x2 : 3	0.2	1	0	0	0.2	13.6(Rp : 13.6 / 0.2 = 68)
Z	0.2	0	0	0	-1.8	93.6

Entrante : - | Sortante : - | Pivot : -

Base	x1 : 4	x2 : 3	x3 : 6	s1 : 0	s2 : 0	CST
s2 : 0	(1/5)/(1/5) = 1	(0)/(1/5) = 0	(0)/(1/5) = 0	(1)/(1/5) = 5	(1/5)/(1/5) = 1	(38/5)/(1/5) = 38
x3 : 6	(3/5)-((-2/5)*(1/5)/(1/5)) = 1	(0)-((-2/5)*(0)/(1/5)) = 0	(1)-((-2/5)*(0)/(1/5)) = 1	(0)-((-2/5)*(1)/(1/5)) = 2	(-2/5)-((-2/5)*(1/5)/(1/5)) = 0	(44/5)-((-2/5)*(38/5)/(1/5)) = 24
x2 : 3	(1/5)-((1/5)*(1/5)/(1/5)) = 0	(1)-((1/5)*(0)/(1/5)) = 1	(0)-((1/5)*(0)/(1/5)) = 0	(0)-((1/5)*(1)/(1/5)) = -1	(1/5)-((1/5)*(1/5)/(1/5)) = 0	(68/5)-((1/5)*(38/5)/(1/5)) = 6
Z	((01)+(61)+(3*0))-(4) = 2	((00)+(60)+(3*1))-(3) = 0	((00)+(61)+(3*0))-(6) = 0	((05)+(62)+(3*-1))-(0) = 9	((01)+(60)+(3*0))-(0) = 0	(038)+(624)+(3*6) = 162