Método Simplex

Ejercicio 1

Restricciones:

Sujeto a:

X1+2x2+2x3+4x4>=40

2x1-x2+x3+2x4>=8

4x1-2x2+x3-x4>=10

Minimizar: 5x1-4x2+6x3+8x4

Desarrollo:

Z= 5x1-4x2+6x3-8x4+0S1+0S2+0S3

Z-5x1+4x2-6x388x4-0S1-0S2-0S3=0

X1+2x2+2x3+4x4+S1=40

2x1-x2+x3+2x4+S2=8

4x1-2x2+x3-x4+S3=10

Desarrollo de la nueva fila

Punto pivote: 2

0.0/2 = 0.0

2.0/2 = 1.0

-1.0/2 = -0.5

1.0/2 = 0.5

2.0/2 = 1.0

0.0/2 = 0.0

1.0/2 = 0.5

0.0/2 = 0.0

8.0/2 = 4.0

 Z = 8

1 - (8 * 0.0) = 1.0

-5 - (8 * 1.0) = -13.0

4 - (8 * -0.5) = 8.0

-6 - (8 * 0.5) = -10.0

8 - (8 * 1.0) = 0.0

0 - (8 * 0.0) = 0.0

0 - (8 * 0.5) = -4.0

0 - (8 * 0.0) = 0.0

0 - (8 * 4.0) = -32.0

S1 = 4

0 - (4 * 0.0) = 0.0

1 - (4 * 1.0) = -3.0

2 - (4 * -0.5) = 4.0

2 - (4 * 0.5) = 0.0

4 - (4 * 1.0) = 0.0

1 - (4 * 0.0) = 1.0

0 - (4 * 0.5) = -2.0

0 - (4 * 0.0) = 0.0

40 - (4 * 4.0) = 24.0

S3 =  -1

0 - (-1 * 0.0) = 0.0

4 - (-1 * 1.0) = 5.0

-2 - (-1 * -0.5) = -2.5

1 - (-1 * 0.5) = 1.5

-1 - (-1 * 1.0) = 0.0

0 - (-1 * 0.0) = 0.0

0 - (-1 * 0.5) = 0.5

1 - (-1 * 0.0) = 1.0

10 - (-1 * 4.0) = 14.0

 

Nueva Fila

Punto pivote: 4

0.0/4 = 0.0

-3.0/4 = -0.75

4.0/4 = 1.0

0.0/4 = 0.0

0.0/4 = 0.0

1.0/4 = 0.25

-2.0/4 = -0.5

0.0/4 = 0.0

24.0/4 = 6.0

 Z = 8

1 - (8 * 0.0) = 1.0

-13 - (8 * -0.75) = -7.0

8 - (8 * 1.0) = 0.0

-10 - (8 * 0.0) = -10.0

0 - (8 * 0.0) = 0.0

0 - (8 * 0.25) = -2.0

-4 - (8 * -0.5) = 0.0

0 - (8 * 0.0) = 0.0

-32 - (8 * 6.0) = -80.0

S4 = -0.5

0 - (-0.5 * 0.0) = 0.0

1 - (-0.5 * -0.75) = 0.625

-0.5 - (-0.5 * 1.0 ) = 0.0

0.5 - (-0.5 * 0.0) = 0.5

1 - (-0.5 * 0.0) = 1.0

0 - (-0.5 * 0.25) = 0.125

0.5 - (-0.5 * -0.5) = 0.25

0 - (-0.5 * 0.0) = 0.0

4 - (-0.5 * 6.0) = 7.0

S3 =  -2.5

0 - (-2.5 * 0.0) = 0.0

5 - (-2.5 * -0.75) = 3.125

-2.5 - (-2.5 * 1.0) = 0.0

1.5 - (-2.5 * 0.0) = 1.5

0 - (-2.5 * 0.0) = 0.0

0 - (-2.5 * 0.25) = 0.625

0.5 - (-2.5 * -0.5) = -0.75

1 - (-2.5 * 0.0) = 1.0

14 - (-2.5 * 6.0) = 29.0