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SENSITIVITY ANALYSIS: COMPUTER SOLUTION 97

3.3 Sensitivity Analysis: Computer Solution

In Section 2.4 we showed how computer packages can be used to solve the GulfGolf
linear programme. Let us demonstrate the use of The Management Scientist in
performing sensitivity analysis by considering the solution to the GulfGolf linear
programme shown in Figure 3.4.

Interpretation of Computer Output
In Appendix 2.2 we discussed the Management Scientist output in the top portion of
Figure 3.4. So, after rounding, we see that the optimal solution is S ¼ 540 standard
bags and D ¼ 252 deluxe bags; the value of the optimal solution is $7668. The
Reduced Costs indicate how much the objective function coefficient of each decision
variable would have to improve before that variable could assume a positive value in
the optimal solution. For the GulfGolf problem, both variables already have positive
values, and so their corresponding reduced costs are zero. In Section 3.4 we will
interpret the reduced cost for a decision variable that does not have a positive value
in the optimal solution.
Immediately following the optimal S and D values and the reduced cost informa-
tion, the computer output provides information about the constraints. Recall that
the problem had four less-than-or-equal-to constraints corresponding to the hours

Figure 3.4 The Management Scientist Solution for the GulfGolf Problem
Objective Function Value = 7667.99463

Variable Value Reduced Costs
-------------- --------------- -----------------
S 539.99841 0.00000
D 252.00113 0.00000

Constraint Slack/Surplus Dual Prices
-------------- --------------- -----------------
1 0.00000 4.37496
2 120.00070 0.00000
3 0.00000 6.93753
4 17.99988 0.00000
EXCEL file
OBJECTIVE COEFFICIENT RANGES
GulfGolf
Variable Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
S 6.30000 10.00000 13.49993
D 6.66670 9.00000 14.28572

RIGHT HAND SIDE RANGES
Constraint Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
1 495.59998 630.00000 682.36316
2 479.99930 600.00000 No Upper Limit
3 580.00146 708.00000 900.00000
4 117.00012 135.00000 No Upper Limit

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