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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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