If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change.
Question
If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change.
Solution
Yes, that's correct. The shadow price, or dual value, represents the rate of improvement in the optimal value of the objective function per unit increase in the right-hand side of a constraint. It is valid only within the sensitivity range for that constraint quantity. If we change the constraint quantity to a value outside this sensitivity range, the shadow price will indeed change. This is because the sensitivity range indicates the range over which the current optimal solution (and hence the shadow price) remains valid. Outside this range, a different solution may become optimal, leading to a change in the shadow price.
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