If we change the constraint quantity to a value outside the sensitivity range for that constraint quantity, the shadow price will change.

In linear programming and optimization, the concept of shadow price provides valuable insights into how sensitive a solution is to changes in the constraints. The shadow price indicates the amount by which the objective function's optimum value would change if the right-hand side of a constraint is increased by one unit.

When the constraint quantity is modified within the sensitivity range, the shadow price remains valid and provides useful information regarding the marginal value of the constraint. However, if this constraint is changed to a value outside the established sensitivity range, the shadow price will likely change as well, indicating that the previous evaluation of the marginal resource has become inaccurate.

Typically, entering a zone outside of this range can lead to a non-linear behavior in the optimization problem, resulting in a need to resolve the linear programming problem entirely. This change signifies that the optimal solution may no longer lie at the current vertex of the feasible region, and a different corner point (or vertex) of the feasible set may yield a new optimal solution.

Overall, adjustments made outside the sensitivity range highlight the importance of understanding optimality conditions and reinforce that sensitivity analysis is crucial for making informed decisions based on linear programming results.