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A-44

Module A

The Simplex Solution Method

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.

    Were any of the constraints originally equations? Why?

  • g.

    What is the value of x2 in this tableau?

3. The following is a simplex tableau for a linear programming problem:

60

50

45

50

0

0

0

0

Quantity

x1

x2

x3

x4

s1

s2

s3

s4

20

0

1

0

0

1

0

0

0

15

0

0

0

1

0

1

0

0

12

1

1/2

0

0

0

0

1/10

0

45

0

0

8

6

0

-6

0

1

1,470

60

30

0

50

0

50

6

0

0

20

45

0

0

- 50

-6

0

c

j

Basic Variables

0 50 60 0

s x x s

1 4 1 4

z j

c j - z j

a. Is this a maximization or a minimization problem? b. What are the values of the decision variables in this tableau? c. What are the values of the slack variables in this tableau? d . W h a t d o e s t h e v a l u e o f 2 0 i n t h e c o l u m n m e a n ? x 2 c j - e. Is this solution optimal? Why? If the solution is not optimal, determine the optimal solution. z j

4. The following is a simplex tableau for a linear programming problem:

cj

M 10 M

Basic Variables

A x A 1 2 3

z j - c j z j

30

2/3

0

1

10

1/3

1

0

100

0

0

1

130M + 100

2M>3 + 10>3

10

2M

2M>3 - 14>3

0

2M - 4

Quantity

8 x1

10

4

x2

x3

1/6

0

0

0

-1>6

0

1

0

0

-1

0

1

-M M>6 - 5>3

-M

M

M

-M M>6 - 5>3

-M

0

0

0 s1

  • -

    1 0 0

0 s2

0 s3

MM

A1

A2

a. Is this a maximization or a minimization problem? b. What is the value of x3 in this tableau? c . W h a t d o e s t h e v a l u e i n t h e c o l u m n o f t h e r o w m e a n ? z j - c j s 2 M > 6 - 5 d. What is the minimum number of additional simplex iterations that this problem must go > 3

through to determine a feasible optimal solution? e. Is this solution optimal? Why? If the solution is not optimal, compute the optimal solution.

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