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A-40

Module A

The Simplex Solution Method

Table A-37 The Final Simplex Tableau

c j

200 160 0

Basic Variables

x x s3 2 1

c j - z j z j

Quantity

8 + ¢/2 4 - ¢/2 48 + 6¢

2,240 + 20¢

0

1

1/2

- 1/18

0

1

0

- 1/2

1/9

0

0

0

6

-2

1

160

200

0

0

0

x1

x2

s1

s2

s3

160

200

20

20/3

0

0

0

- 20

- 20/3

0

8 + ¢>2 Ú 0 4 - ¢>2 Ú 0 48 + 6¢ Ú 0

are solved for ¢:

8 + ¢>2 Ú 0 ¢>2 Ú -8 ¢ Ú -16

and

4 - ¢>2 Ú 0

  • -

    ¢>2 Ú -4

¢ …8

and

48 + 6¢ Ú 0 6¢ Ú -48 ¢ Ú -8

Since

q1 = 40 + ¢

then

¢ = q1 - 40

These values are substituted into the inequalities ¢ Ú -16, ¢ … 8, and ¢ Ú -8 as follows:

¢ Ú -16 q1 - 40 Ú -16 q1 Ú 24 ¢ …8 q1 - 40 8 q1 48 ¢ Ú -8 q1 - 40 Ú -8 q1 Ú 32

Summarizing these inequalities, we have 24 32 q1 48

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