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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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