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MORE THAN TWO DECISION VARIABLES 113

Figure 3.13 The Management Scientist Solution for the KCC Problem

Objective Function Value = 597.297

Variable Value Reduced Costs
-------------- --------------- -----------------
S 3.514 0.000
E 0.946 0.000
A 1.541 0.000
Constraint Slack/Surplus Dual Prices
-------------- --------------- -----------------
1 0.000 –121.622
2 3.554 0.000
3 0.000 –195.946
EXCEL file 4 0.000 91.92
KCC OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
S –39.286 25.00 No Upper Limit
E No Lower Limit 50.00 92.50
A 152.174 300.00 No Upper Limit

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit
------------ --------------- --------------- ---------------
1 1.143 3.000 3.368
2 No Lower Limit 6.000 9.554
3 2.100 4.000 4.875
4 5.562 6.000 8.478

Note that after rounding, this result is the same as the objective function value in the
computer output (Figure 3.13).
Looking at the Slack/Surplus section of the computer output, we find a value of
3.554 for constraint 2. Because constraint 2 is a greater-than-or-equal-to constraint,
3.554 is the surplus; the optimal solution exceeds the minimum daily diet requirement
for ingredient B (six units) by 3.554 units. Because the surplus values for constraints 1
and 3 are both zero, we see that the optimal diet just meets the minimum require-
ments for ingredients A and C; moreover, a slack value of zero for constraint 4 shows
that the optimal solution provides a total daily feed weight of six kilos.
The dual price (after rounding) for the ingredient A constraint (constraint 1)
is 121.62. To interpret this value properly, we first look at the sign; it is negative,
and so we know that increasing the right-hand side of constraint 1 will cause the
solution value to worsen. In a minimization problem, ‘worsen’ means that the total
daily cost will increase, and therefore, a one-unit increase in the right-hand side of
constraint 1 will increase the total cost of the daily diet by 121.62 sh. Conversely, it is
also correct to conclude that a decrease of one unit in the right-hand side will
decrease the total cost by the same amount. Looking at the RIGHT HAND SIDE
RANGES section of the computer output, we see that these interpretations are valid
as long as the right-hand side is between 1.143 and 3.368.

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