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SOLVING LINEAR PROGRAMMES WITH THE MANAGEMENT SCIENTIST 83

The Management The user entries in the data input worksheet are shown in Figure 2.26. The output
Scientist interprets from The Management Scientist is shown in Figure 2.25. When entering the prob-
the < symbol as and lem data, zero coefficients do not have to be entered. The original problem can be
the > symbol as .
edited or changed by selecting the Edit menu. Finally, printed output can be
obtained by selecting the Solution menu and then selecting the Print option.
The Management Scientist output is shown in Figure 2.25. First, note the number
7667.99417, which appears to the right of Objective Function Value. Rounding this
value, we can conclude that the optimal solution to this problem will provide a profit
of $7668. Directly below the objective function value, we find the values of the
decision variables at the optimal solution. After rounding we have S ¼ 540 standard
bags and D ¼ 252 deluxe bags as the optimal production quantities. The informa-
tion in the Reduced Costs column indicates how much the objective function
coefficient of each decision variable would have to improve before it would be
possible for that variable to assume a positive value in the optimal solution. If a
decision variable is already positive in the optimal solution, its reduced cost is zero.
For the GulfGolf problem, the optimal solution is S ¼ 540 and D ¼ 252. Both
variables already have positive values; therefore, their corresponding reduced costs
are zero. In Chapter 3 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 status of the constraints.
Recall that the GulfGolf problem had four less-than-or-equal-to constraints corre-
sponding to the hours available in each of four production departments. The

Figure 2.25 The Management Scientist Solution for the GulfGolf Problem

EXCEL file Objective Function Value = 7667.99417
GULFGOLF
Variable Value Reduced Costs
S 539.99842 0.00000
D 252.00110 0.00000

Constraint Slack/Surplus Dual Prices
1 0.00000 4.37496
2 120.00071 0.00000
3 0.00000 6.93753
4 17.99988 0.00000
OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit
S 6.30000 10.00000 13.49993
D 6.66670 9.00000 14.28571

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit
1 495.60000 630.00000 682.36316
2 479.99929 600.00000 No Upper Limit
3 580.00140 708.00000 900.00000
4 117.00012 135.00000 No Upper Limit

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