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108 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

Figure 3.10 Excel Solution for the Modified GulfGolf Problem with the Coefficient of D increased by
$1.15004
Original
Name Value Final Value
Maximize Total Profit Standard 0 8299.8
Original
Name Value Final Value
Bags produced Standard 0 403.7831816
Bags produced Deluxe 0 222.811955
Bags produced Lightweight 0 155.6747724

Name Cell Value Status Slack
Cutting and Dyeing 630 Binding 0
Hours Used (LHS)
Sewing Hours 543.2422496 Not Binding 56.75775038
Used (LHS)
Finishing Hours
Used (LHS) 708 Binding 0
Inspection and
Packaging Hours 135 Binding 0
Used (LHS)

Adjustable Cells
Final Reduced Objective Allowable Allowable
Name Value Cost Coefficient Increase Decrease
Bags produced 403.7831816 0 10 2.510712954 2.34002E–05
Standard
Bags produced 222.811955 0 10.15004 5.257854737 1.3E–05
Deluxe
Bags produced 155.6747724 0 12.85 1.06364E–05 2.196870893
Lightweight
Constraints
Final Shadow Constraint Allowable Allowable
Name Value Price R.H. Side Increase Decrease
Cutting and 630 3.16218E–05 630 52.36315884 91.6
Dyeing Hours
Used (LHS)
Sewing Hours 543.2422496 0 600 1E+30 56.75775038
Used (LHS)
Finishing Hours 708 8.099979973 708 144.6315789 127.9986
Used (LHS)
Inspection and 135 18.99997892 135 16.1540957 17.99988187
Packaging Hours
Used (LHS)

some of the employees in the cutting and dyeing department could be used to
perform certain operations in either the finishing department or the inspection
and packaging department. In the future, management may want to explore the
possibility of cross-training employees so that unused capacity in one department
could be shifted to other departments.
Suppose that after reviewing the solution shown in Figure 3.9, management insist
that they will not consider any solution that does not include the production of some
deluxe bags. Management then decides to add the requirement that the number of
deluxe bags produced must be at least 30 per cent of the number of standard bags
produced. Writing this requirement using the decision variables S and D, we obtain:

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