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Table A-23 The Third Simplex Tableau

c j

  • -

    M

200 400

Basic Variables

A1

x

2

x

1

z j

c j - z j

400

200

0

0

-M

Quantity

x1

x2

s1

s2

A1

5

0

0

1/8

-3>4

1

5

0

1

-1>8

-1>4

0

20

1

0

0

1

0

Irregular Types of Linear Programming Problems

A-23

9,000 - 5M

400

200

-25 - M>8

350 + 3M>4

-M

0

0

25 + M>8

-350 - 3M>4

0

Table A-24 The Optimal Simplex Tableau

c j

0

200 400

Basic Variables

s1

x

2

x

1

z j

c j - z j

400

Quantity

x1

40

0

10

0

20

1

10,000

400

0

200

0

0

x2

s1

s2

0

1

-6

1

0

-1

0

0

1

200

0

200

0

0

- 200

The solution for the leather shop problem is (see Table A-24)

s 1 = 4 0 e x t r a y d . 2 o f l e a t h e r x 2 = 1 0 p i e c e s o f l u g g a g e x 1 = 2 0 b r i e f c a Z = $10,000 profit per month s e s

It is now possible to summarize a set of rules for transforming all three types of model constraints:

Objective Function Coefficient

Constraint

Adjustment

MAXIMIZATION

MINIMIZATION

= Ú

Add a slack variable Add an artificial variable Subtract a surplus variable

and add an artificial variable

0

  • -

    M

0

  • -

    M

0 M 0 M

Irregular Types of Linear Programming Problems

For irregular problems the general simplex procedure does not always apply.

The basic simplex solution of typical maximization and minimization problems has been shown in this module. However, there are several special types of atypical linear program- ming problems. Although these special cases do not occur frequently, they will be described within the simplex framework so that you can recognize them when they arise.

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