Page 109 -

GRAPHICAL SENSITIVITY ANALYSIS 89

Figure 3.1 Graphical Solution of GulfGolf Problem with Slope of Objective Function
Line Between Slopes of Lines A and B; Extreme Point fi Is Optimal

D
Line B
(coincides with the
800
finishing constraint line
1S + 0.6667 D = 708)

600 5 Objective Function Line
Number of Deluxe Bags 400 4 Line A
for 10S + 9D

the cutting and dyeing
constraint line
Feasible 3 (coincides with
0.7S + 1D = 630)
200 Region

1 2
S
0 200 400 600 800
Number of Standard Bags

Thus, extreme point fi will be the optimal solution as long as:

Slope of line B slope of the objective function line slope of line A
In Figure 3.1 we see that the equation for line A, the cutting and dyeing constraint
line, is:

0:7S þ 1D ¼ 630
By solving this equation for D, we can write the equation for line A in its slope-
intercept form, which yields:
D ¼ 0:7S þ 630
" "
Slope of Intercept of
line A line A on
D axis

Thus, the slope for line A is 0.7, and its intercept on the D axis is 630.
The equation for line B in Figure 3.1 is:

1S þ 0:6667D ¼ 708
Solving for D provides the slope-intercept form for line B. Doing so yields:
0:6667D ¼ 1S þ 708
D ¼ 1:5S þ 1062

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.