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Although we do not perform the analysis here, if you increase resource A to 801
hours, I assure you that the solution will not change since it is non-binding and has
slack of 61.81 hours.
These types of changes in the problem formulation are a form of sensitivity anal-
ysis. It would be convenient to have access to the results of these analyses without
having to perform each individual change in the formulation. As you might guess,
Excel does provide this type of analysis. It comes in the form of one of the three
Report options in the Solver Results dialogue box (see Exhibit 9.6)—the Sensitivity
Report . Exhibit 9.9 shows the Sensitivity Report for the YRA formulation. Let us
focus on the Constraints section of the report, and particularly the column entitled
Shadow Price . Shadow prices are associated with constraints and result from the
solution algorithm used to determine an optimal solution. Each of our four resource
hour constraints can have a shadow price and it can be interpreted as the bene-
ﬁt to the objective function if the RHS of a constraint is increased by one unit.
Additionally, only binding constraints have shadow prices; thus, the resource A con-
straint will not have a shadow price since it is non-binding. Resource B, C, and D
constraints do have a shadow price due to their binding condition, as can be seen in
Exhibit 9.9.
As we examine the shadow prices, we can see a very interesting similarity. The
shadow price of an additional hour of resource B is 3,686.44, which is precisely the
change in objective function value we obtained earlier when we manually increased
the RHS to 901. The shadow prices of resources C and D are less, 699.15 and
152.54, respectively. Thus, if I am allowed to increase any RHS of the four resource
Exhibit 9.9 Sensitivity report for YRA
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