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EXTREME POINTS AND THE OPTIMAL SOLUTION 53

to be re-solved later, changes in some of the data constraints in the linear programming model even
might make a previously redundant constraint a though at some point in time one or more of the
binding constraint. Thus, we recommend keeping all constraints may be redundant.

2.3 Extreme Points and the Optimal Solution

Suppose that the profit contribution for the company’s standard golf bag is reduced
from $10 to $5 per bag, while the profit contribution for the deluxe golf bag and all
the constraints remain unchanged. The complete linear programming model of this
new problem is identical to the mathematical model in Section 2.1, except for the
revised objective function:
Max 5S þ 9D

How does this change in the objective function affect the optimal solution to the
problem? Figure 2.12 shows the graphical solution of this new problem with the
revised objective function. Note that without any change in the constraints, the
feasible region does not change. However, the profit lines have been altered to
reflect the new objective function.
By moving the profit line in a parallel manner toward higher profit values, we find
the optimal solution as shown in Figure 2.12. The values of the decision variables at
this point are S ¼ 300 and D ¼ 420. The reduced profit contribution for the stand-
ard bag caused a change in the optimal solution. In fact, as you may have suspected,
we are cutting back the production of the lower-profit standard bags and increasing
the production of the higher-profit deluxe bags.

Figure 2.12 Optimal Solution for the GulfGolf Problem with an Objective Function
of 5S+ 9D

D

600
Optimal Solution
(S = 300, D = 420)
Number of Deluxe Bags 400 (0, 300) Maximum Profit Line: 5S + 9D = 5280

200

5S + 9D = 2700
(540, 0)

S
0 200 400 600 800
Number of Standard Bags

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