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GRAPHICAL SENSITIVITY ANALYSIS 91

In the original problem for GulfGolf, the standard bag had a profit contribution
of $10. The resulting optimal solution was 540 standard bags and 252 deluxe bags.
The range of optimality for C S tells management that, with other coefficients
unchanged, the profit contribution for the standard bag can vary between $6.30
and $13.50 and the production quantities of 540 standard bags and 252 deluxe bags
will remain optimal. Note, however, that even though the production quantities will
not change, the total profit contribution (the value of objective function) will change
due to the change in profit contribution per standard bag.
These calculations can be repeated, holding the profit contribution for stand-
ard bags constant at C S ¼ 10. In this case, the range of optimality for the deluxe-
bag profit contribution can be determined. Check to see that this range is 6.67
C D 14.29.
In cases where the rotation of the objective function line about an optimal
extreme point causes the objective function line to become vertical,therewill
either be no upper limit or no lower limit for the slope as it appears in the form
of expression (3.2). To show how this special situation can occur, suppose that the
objective function for the GulfGolf problem is 18C S +9C D . In this case, extreme
point › in Figure 3.2 provides the optimal solution. Rotating the objective function
line anticlockwise around extreme point › provides an upper limit for the slope
when the objective function line coincides with line B. We showed previously that
the slope of line B is 1.5, so the upper limit for the slope of the objective function
line must be 1.5. However, rotating the objective function line clockwise results
in the slope becoming more and more negative, approaching a value of minus

Figure 3.2 Graphical Solution of GulfGolf Problem with an Objective Function of 18S+
9D; Optimal Solution At Extreme Point ›

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

Number of Deluxe Bags 600 5 4 Vertical

for 18S + 9D

Line
400

Feasible 3
200
Region
New Optimal
Solution
1 2
S
0 200 400 600 800
Number of Standard Bags

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