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Sensitivity Analysis

A-41

The value 24 can be eliminated, since q1 must be greater than 32; thus,

32 q1 48

As long as q1 remains in this range, the present basic solution variables will remain the same and feasible. However, the quantity values of those basic variables may change. In other words, although the variables in the basis remain the same, their values can change.

To determine the range for q2 (where q2 = 216 + ¢), the s2 column values are used to develop the ¢ inequalities:

8 - ¢>18 Ú 0 4 + ¢>9 Ú 0 48 - 2¢ Ú 0

The inequalities are solved as follows:

8 - ¢>18 Ú 0

  • -

    ¢>18 Ú -8

¢ … 144

4 + ¢>9

Ú0

¢>9

Ú -4

¢

Ú -36

48 - 2¢

Ú0

-2¢

Ú -48

¢ … 24

¢ … 144

q2 - 216

144

2 q

360

Since

That is,

¢ … 24 q2 - 216 24 q2 240

180 q2 240 360

¢Ú

- 36

q2 - 216 Ú

- 36

2 qÚ

180

Substituting this value into the inequalities ¢ … 144, ¢ Ú -36, and ¢ … 24 gives a range of possible values for q2:

we have

q2 = 216 + ¢

¢ = q2 - 216

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