Page 246 -

226 CHAPTER 5 LINEAR PROGRAMMING: THE SIMPLEX METHOD

Figure 5.2 Feasible Region and Extreme Points for the HighTech Industries Problem

x 2
60

50 Warehouse Capacity

40
Portable 30

5 4 Display Units
20

3
10 Feasible
Region Assembly Time

1 2
10 20 30 40 50 x 1
Deskpro

row – that for s 3 equals 6.25. One of the managerial benefits of the Simplex
method is that virtually every part of the tableau can be used to help management
understand the consequences of decisions. Here we see that s 3 takes a negative value
of E6.25. The interpretation of this is straightforward; s 3 has just been taken out of
the solution and is non-basic with a zero value. But this coefficient tells us that if we
were to force s 3 back into the situation at this stage, it would have a negative impact
on the objective function. In other words, if we insisted on having unused warehouse
space (which is what s 3 measures), then each square metre of unused space will
effectively cost HighTech E6.25 in lost profit contribution since the only way of
freeing up warehouse space at this stage is to reduce production of x 1 .
To determine which variable will be removed from the basis when x 2 enters, we
must calculate for each row i the ratio b i /a i2 (remember, though, that we should
calculate this ratio only if a i2 is greater than zero); then we select the variable to
leave the basis that corresponds to the minimum ratio. As before, we will show these
ratios in an extra column of the simplex tableau:

x 1 x 2 s 1 s 2 s 3
b
Basis c B 50 40 0 0 0 a i2
37:5
0 0 3.125 1 0 0.375 37.5 ¼ 12
3:125
s 1
20
s 2 0 0 1 0 1 0 20 ¼ 20
1
37:5
x 1 50 1 0.625 0 0 0.125 37.5 ¼ 60
0:625
50 31.25 0 0 6.25 1 875
z j
0 8.75 0 0 6.25
c j – z j

Copyright 2014 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has
deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.