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85
T
EACHING
S
UGGESTIONS
Teaching Suggestion 7.1:
Draw Constraints for a
Graphical LP Solution.
Explain constraints of the three types (
#
,
5
,
$
) carefully the first
time you present an example. Show how to find the
X
1
,
X
2
inter
cepts so a straight line can be drawn. Then provide some practice
in determining which way the constraints point. This can be done
by picking a few
X
1
,
X
2
coordinates at random and indicating
which direction fulfills the constraints.
Teaching Suggestion 7.2:
Feasible Region Is a Convex Polygon.
Explain Dantzing’s discovery that all feasible regions are convex
(bulge outward) polygons (manysided figures) and that the opti
mal solution must lie at one of the corner points. Draw both con
vex and concave figures to show the difference.
Teaching Suggestion 7.3:
Using the IsoProfit Line Method.
This method can be much more confusing than the corner point ap
proach, but it is faster once students feel comfortable drawing the
profit line. Start your first line at a profit figure you know is lower
than optimal. Then draw a series of parallel lines, or run a ruler paral
lel, until the furthest corner point is reached. See Figures 7.6 and 7.7.
Teaching Suggestion 7.4:
QA in Action Boxes in the LP Chapters.
There are a wealth of motivating tales of realworld LP applica
tions in Chapters 7–9. The airline industry in particular is a major
LP user.
Teaching Suggestion 7.5:
Feasible Region for the
Minimization Problem.
Students often question the open area to the right of the constraints
in a minimization problem such as that in Figure 7.10. You need
to explain that the area is not unbounded to the right in a mini
mization problem as it is in a maximization problem.
Teaching Suggestion 7.6:
Infeasibility.
This problem is especially common in large LP formulations since
many people will be providing input constraints to the problem.
This is a realworld problem that should be expected.
Teaching Suggestion 7.7:
Alternative Optimal Solutions.
This issue is an important one that can be explained in a positive
way. Managers appreciate having choices of decisions that can be
made with no penalty. Students can be made aware that alternative
optimal solutions will arise again in the transportation model, as
signment model, integer programming, and the chapter on net
work models.
Teaching Suggestion 7.8:
Importance of Sensitivity Analysis.
Sensitivity analysis should be stressed as one of the most important
LP issues. (Actually, the issue should arise for discussion with every
model). Here, the issue is the source of data. When accountants tell
you a profit contribution is $8.50 per unit, is that figure accurate
within 10% or within 10¢? The solution to an LP problem can
change dramatically if the input parameters are not exact. Mention
that sensitivity analysis also has other names, such as righthand
side ranging, postoptimality analysis, and parametric programming.
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 Spring '09
 smith

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