1. What is Sensitivity Analysis in Linear Programming?

Definition: Sensitivity analysis measures how changes in constraints affect the optimal solution in linear programming problems.

Purpose: It helps decision-makers understand the robustness of their solution and how much constraints can change before the optimal solution changes.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \(\Delta \text{Objective}\) — Change in objective function value (units depend on context)
• \(\Delta \text{Constraint}\) — Change in constraint value (units depend on context)

Explanation: The ratio shows how much the objective function changes per unit change in the constraint.

3. Importance of Sensitivity Analysis

Details: Understanding sensitivity helps in decision-making when parameters are uncertain or likely to change, and in identifying critical constraints.

4. Using the Calculator

Tips: Enter the change in objective function value and the corresponding change in constraint value. The constraint change must be non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a high sensitivity value mean?
A: A high value means the objective function is very responsive to changes in this constraint.

Q2: Can sensitivity be negative?
A: Yes, negative sensitivity indicates an inverse relationship between the constraint and objective.

Q3: How is this different from shadow price?
A: Shadow price is the sensitivity at the optimal solution, while this calculator computes general sensitivity.

Q4: What units does sensitivity have?
A: Units are (objective function units)/(constraint units).

Q5: When would sensitivity be zero?
A: When changes in the constraint don't affect the objective function (non-binding constraint).