**Sensitivity Analysis in Linear Programming:**

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**Definition:**

Sensitivity analysis in linear programming involves examining how changes in the coefficients of the objective function, the right-hand side values of constraints, or the coefficients of the decision variables affect the optimal solution and related parameters.

**Key Aspects of Sensitivity Analysis:**

**Objective Function Coefficients:**

*Effect:*Changes in the coefficients of the objective function impact the optimal solution.*Analysis:*Determine how much the objective function coefficient can change without changing the current optimal solution. This is often expressed as the shadow price or dual value.

**Right-hand Side Values (RHS) of Constraints:**

*Effect:*Changes in the RHS values of constraints impact the feasibility and shadow prices.*Analysis:*Evaluate the allowable increase or decrease in the RHS values without changing the current optimal solution. This is expressed as the range of feasibility or range of optimality.

**Coefficients of Decision Variables (Technological Coefficients):**

*Effect:*Changes in the coefficients of decision variables impact the shadow prices.*Analysis:*Assess the impact on the shadow prices associated with changes in the coefficients of the decision variables. This helps in understanding the rate of change in the objective function value concerning a unit change in a decision variable’s coefficient.

**Steps in Sensitivity Analysis:**

**Solve the Original Linear Programming Problem:**

- Find the optimal solution using the original coefficients and parameters.

**Identify the Key Coefficients:**

- Determine which coefficients (objective function, RHS values, or decision variable coefficients) you want to analyze for sensitivity.

**Formulate Perturbed Problems:**

- Create perturbed (modified) versions of the original problem by changing the identified coefficients.

**Solve Perturbed Problems:**

- Solve each perturbed problem to find new optimal solutions.

**Analyze Changes:**

- Evaluate how changes in coefficients impact the optimal solution, shadow prices, and feasibility.

**Interpret Results:**

- Draw conclusions about the robustness of the solution and the system’s sensitivity to changes in coefficients.

Sensitivity analysis provides valuable insights for decision-makers, helping them understand the stability of the optimal solution and make informed decisions in the face of uncertainty or changing parameters in a linear programming model.