Tarea de investigación: MAXIMIZAR: 1 X1 + 3 X2 + 2 X3

MAXIMIZAR: 1 X1 + 3 X2 + 2 X3

[pic 1]

MAXIMIZAR: 1 X1 + 3 X2 + 2 X3 + 0 X4 + 0 X5 + 0 X6

3 X1 + 1 X2 + 2 X3 ≤ 7
1 X1 + 2 X2 + 0 X3 ≤ 6
4 X1 + 3 X2 + 8 X3 ≤ 40

3 X1 + 1 X2 + 2 X3 + 1 X4 = 7
1 X1 + 2 X2 + 1 X5 = 6
4 X1 + 3 X2 + 8 X3 + 1 X6 = 40

X1, X2, X3 ≥ 0

X1, X2, X3, X4, X5, X6 ≥ 0

Tabla 1

Base

z

b

X1

X2

X3

X4

X5

X6

X4

0

7

3

1

2

1

0

0

X5

0

6

1

2

0

0

1

0

X6

0

40

4

3

8

0

0

1

Z

0

-1

-3

-2

0

0

0

Tabla 2

Base

z

b

X1

X2

X3

X4

X5

X6

X4

0

4

2.5

0

2

1

-0.5

0

X2

3

3

0.5

1

0

0

0.5

0

X6

0

31

2.5

0

8

0

-1.5

1

Z

9

0.5

0

-2

0

1.5

0

Tabla 3

Base

z

b

X1

X2

X3

X4

X5

X6

X3

2

2

1.25

0

1

0.5

-0.25

0

X2

3

3

0.5

1

0

0

0.5

0

X6

0

15

-7.5

0

0

-4

0.5

1

Z

13

3

0

0

1

1

0

MAXIMIZAR: 1 X1 + 3 X2 + 2 X3

[pic 2]

MAXIMIZAR: 1 X1 + 3 X2 + 2 X3 + 0 X4 + 0 X5 + 0 X6

3 X1 + 1 X2 + 2 X3 ≤ 4
1 X1 + 2 X2 + 0 X3 ≤ 5
4 X1 + 3 X2 + 8 X3 ≤ 10

3 X1 + 1 X2 + 2 X3 + 1 X4 = 4
1 X1 + 2 X2 + 1 X5 = 5
4 X1 + 3 X2 + 8 X3 + 1 X6 = 10

X1, X2, X3 ≥ 0

X1, X2, X3, X4, X5, X6 ≥ 0

Tabla 3

Base

Z

b

X1

X2

X3

X4

X5

X6

X4

0

7 / 8

15 / 8

0

0

1

-1 / 8

-1 / 4

X2

3

5 / 2

1 / 2

1

0

0

1 / 2

0

X3

2

5 / 16

5 / 16

0

1

0

-3 / 16

1 / 8

Z

65 / 8

9 / 8

0

0

0

9 / 8

1 / 4

Tabla 2

Base

Z

b

X1

X2

X3

X4

X5

X6

X4

0

4

2.5

0

0.5

1

-0.5

0

X2

3

3

0.5

1

1.5

0

0.5

0

X6

0

1

2.5

0

-0.5

0

-1.5

1

Z

9

0.5

0

2.5

0

1.5

0

MAXIMIZAR: 1 X1 + 3 X2 + 2 X3 + 8 X4 + 15 X5

[pic 3]

MAXIMIZAR: 1 X1 + 3 X2 + 2 X3 + 8 X4 + 15 X5 + 0 X6 + 0 X7 + 0 X8

3 X1 + 1 X2 + 2 X3 + 2 X4 + 4 X5 ≤ 7
1 X1 + 2 X2 + 0 X3 + 5 X4 + 1 X5 ≤ 6
4 X1 + 3 X2 + 8 X3 + 1 X4 + 7 X5 ≤ 10

3 X1 + 1 X2 + 2 X3 + 2 X4 + 4 X5 + 1 X6 = 7
1 X1 + 2 X2 + 5 X4 + 1 X5 + 1 X7 = 6
4 X1 + 3 X2 + 8 X3 + 1 X4 + 7 X5 + 1 X8 = 10

X1, X2, X3, X4, X5 ≥ 0

X1, X2, X3, X4, X5, X6, X7, X8 ≥ 0