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Problems

10

2

6

0

0

0

Quantity

x1

x2

x3

s1

s2

s3

10

1

0

-2

1

-1>2

0

40

0

1

2

0

1/2

0

30

0

0

8

-3

3/2

1

420

10

2

16

2

4

0

0

0

- 10

-2

-4

0

Problems

A-43

as shown in this example, except that the value of qi - ¢ would be used instead of qi + ¢ when computing the sensitivity range for qi.

1. Following is a simplex tableau for a linear programming model:

z j

c j - z j

x

1

x

2

c j

Basic Variables

10 2 0

s

3

6

20

12

0

0

Quantity

x1

x2

x3

s1

s2

20

1

1

0

0

0

10

0

1/3

1

0

-1>6

10

0

1/3

0

1

-1>6

240

6

10

12

0

-2

0

- 10

0

0

-2

  • a.

    Is this a maximization or a minimization problem? Why?

  • b.

    What is the solution given in this tableau?

  • c.

    Is the solution given in this tableau optimal? Why?

    • a.

      What is the solution given in this tableau?

    • b.

      Is the solution in this tableau optimal? Why?

    • c.

      What does x3 equal in this tableau? s2?

    • d.

      Write out the original objective function for the linear programming model, using only decision variables.

    • e.

      How many constraints are in the linear programming model?

    • f.

      Explain briefly why it would have been difficult to solve this problem graphically.

  • 2.

    The following is a simplex tableau for a linear programming model:

c

j

Basic Variables

6 12 0

x x s

1 3 1

z j

z j - c j

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