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MORE THAN TWO DECISION VARIABLES 107

Figure 3.9 Excel Solution for the Modified GulfGolf Problem
Original
Name Value Final Value
Maximize Total Profit 0 8299.8
Standard
Original
Name Value Final Value
Bags produced Standard 0 280
Bags produced Deluxe 0 0
Bags produced Lightweight 0 428

Name Cell Value Status Slack

Cutting and Dyeing 538.4 Not Binding 91.6
Hours Used (LHS)
Sewing Hours 568 Not Binding 32
Used (LHS)
Finishing Hours 708 Binding 0
Used (LHS)
Inspection and Packaging 135 Binding 0
Hours Used(LHS)
Adjustable Cells
Final Reduced Objective Allowable Allowable
Name Value Cost Coefficient Increase Decrease
Bags produced 280 0 10 2.070069297 4.86
Standard
Bags produced 0 –1.150026998 9.000000002 1.150026998 1E+30
Deluxe
Bags produced 428 0 12.85 12.15 0.940932891
Lightweight
Constraints
Final Constraint Allowable Allowable
Name Value Shadow Price R.H. Side Increase Decrease
Cutting and Dyeing 538.4 0 630 1E+30 91.6
Hours Used (LHS)
Sewing Hours 568 0 600 1E+30 32
Used (LHS)
Finishing Hours 708 8.1 708 144.6315789 168
Used (LHS)
Inspection and 135 19 135 9.6 64.2
Packaging Hours
Used (LHS)

EXCEL file
contribution for D increases by at least $1.15 the value of D will remain at zero in
GULFGOLF
the optimal solution.
MODIFIED
Suppose we increase the coefficient of D by $1.1500 and then re-solve the problem.
Figure 3.10 shows the new solution. We note that D has now entered the solution
(although the value of the objective function remains unchanged indicating an alter-
native optimal solution) and all three variables have a reduced cost coefficient of 0.
Returning to Figure 3.9 we note that the shadow prices for constraints 3 and 4 are
8.1 and 19, respectively, indicating that these two constraints are binding in the
optimal solution. So, each additional hour in the finishing department would
increase the value of the optimal solution by $8.10 and each additional hour in the
inspection and packaging department would increase the value of the optimal
solution by $19.00. Because of a slack of 91.6 hours in the cutting and dyeing
department and 32 hours in the sewing department (see Figure 3.9), management
might want to consider the possibility of redeploying these unused hours in the
finishing or inspection and packaging departments. For example, it may be that

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