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A-38

Module A

The Simplex Solution Method

d o e s n o t b e c o m e a m u l t i p l e o f t h e r o w . T h u s , t h e c h a n g e w i l l s h o w u p i n o n l y o n e c o l - u m n i n t h e r o w . c j - z j ¢ z j

Changes in Constraint Quantity Values To demonstrate the effect of a change in the quantity values of the model constraints, we will again use the Hickory Furniture Company example:

maximize Z = 160x1 + 200x2 subject to

o f l a b o r o f w o o d o f s t o r a g e s p a c e x 1 , x 2 Ú 0 2 4 x 1 + 1 2 x 2 2 4 0 f t . 2 1 8 x 1 + 1 8 x 2 2 1 6 b d . f t . 2 x 1 + 4 x 2 4 0 h r .

The quantity values 40, 216, and 240 will be represented symbolically as qi. Thus, q1 = 40, q2 = 216, and q3 = 240. Now consider a ¢ change in q2. For example, let us change q2 = 216 by ¢ = 18. In other words, q2 is changed from 216 board feet to 234 board feet. The effect of this change is shown graphically in Figure A-11.

Figure A-11 A ¢ change in q2

x2

20

Original optimal solution

15

10

New optimal solution with change in q2

A

B

B'

C'

5

C

0

D

5

10

15

20

x1

In Figure A-11 a change in q2 is shown to have the effect of changing the feasible solu- tion area from 0ABCD to 0AB¿C¿D. Originally, the optimal solution point was B; however, the change in q2 causes B¿ to be the new optimal solution point. At point B the optimal solution is

s 1 a n d s 2 = 0 s 3 = 4 8 x 2 = 8 Z = $2,240 x 1 = 4

At point B¿ the new optimal solution is

x 2 = 7 x 1 = 6

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