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50 CHAPTER 2 AN INTRODUCTION TO LINEAR PROGRAMMING

Figure 2.11 Feasible Solutions for the Constraint R T 0

T

300

200
R – T = 0
(100, 100)

100

(0, 0)

0 R
100 200 300

As another example, consider a problem involving two decision variables, R and
T. Suppose that the number of units of R produced had to be at least equal to the
number of units of T produced. A constraint enforcing this requirement is:

R T
or
R T 0

Can you graph a To find all solutions satisfying the constraint as an equality, we first set R ¼ 0 and
constraint line when the solve for T. This result shows that the origin (T ¼ 0, R ¼ 0) is on the constraint line.
origin is on the constraint Setting T ¼ 0 and solving for R provides the same point. However, we can obtain a
line? Try Problem 4.
second point on the line by setting T equal to any value other than zero and then
solving for R. For instance, setting T ¼ 100 and solving for R, we find that the point
(T ¼ 100, R ¼ 100) is on the line. With the two points (R ¼ 0, T ¼ 0) and (R
¼ 100, T ¼ 100), the constraint line R T ¼ 0 and the feasible solutions for R
T 0 can be plotted as shown in Figure 2.11.

Summary of the Graphical Solution Procedure for Maximization
Problems

For additional practise in As we have seen, the graphical solution procedure is a method for solving two-
using the graphical variable linear programming problems such as the GulfGolf problem. The steps of
solution procedure, try
Problem 13 a-d. the graphical solution procedure for a maximization problem are summarized
here:
1 Draw a graph of the feasible solutions for all of the constraints.
2 Determine the feasible region by identifying the solutions that satisfy all the
constraints simultaneously.
3 Choose an arbitrary (but convenient) value for the objective function.

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