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GRAPHICAL SOLUTION PROCEDURE 49

on the line is not always as easy as shown in the GulfGolf problem. For example,
suppose a company manufactures two models of a small handheld computer: the
Assistant (A) and the Professional (P). Management needs 50 units of the Professio-
nal model for its own salesforce, and expects sales of the Professional to be at most
one-half of the sales of the Assistant. A constraint enforcing this requirement is:
P 50 0:5A
or
2P 100 A
or

2P A 100
Using the equality form and setting P ¼ 0, we find the point (P ¼ 0, A ¼ 100)
is on the constraint line. Setting A ¼ 0, we find a second point (P ¼ 50, A ¼ 0)
on the constraint line. If we have drawn only the nonnegative (P 0, A 0)
portion of the graph, the first point (P ¼ 0, A ¼ 100) cannot be plotted
because A ¼ 100 is not on the graph. Whenever we have two points on the
line, but one or both of the points cannot be plotted in the nonnegative portion
of the graph, the simplest approach is to enlarge the graph. In this example, the
point (P ¼ 0, A ¼ 100) can be plotted by extending the graph to include the
negative A axis. Once both points satisfying the constraint equation have been
located, the line can be drawn. The constraint line and the feasible solutions for
the constraint 2P A 100 are shown in Figure 2.10.

Figure 2.10 Feasible Solutions for the Constraint 2P A 100

A

300

200

2 P – A = 100

100

(50, 0)
0 P
100 200 300

(0, –100)
–100

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