# Opeation Research 9: Duality and Post Optimality Analysis | Summary and Q&A

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December 28, 2021
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Solomon Getachew
Opeation Research 9: Duality and Post Optimality Analysis

## TL;DR

Duality allows us to find solutions to linear programming problems by solving the dual, and post-optimality analysis helps examine changes after reaching the optimal solution.

## Key Insights

• ๐ป Duality in linear programming allows us to find solutions to the primal problem by solving the dual.
• ๐ฑ Post-optimality analysis helps examine changes after reaching the optimal solution and provides insights into the sensitivity of the optimal solution to changes in input parameters.
• ๐ฃ Post-optimality analysis can answer questions about the impact of changes in objective function coefficients or constraints on the optimal solution.
• ๐งก The range of changes that will not affect the optimal solution can be determined through post-optimality analysis.
• ๐ถ Changes in the primal problem, such as variations in objective function coefficients or the addition of new constraints, can be analyzed using duality and post-optimality analysis.
• ๐ฃ By conducting post-optimality analysis, managers can make informed decisions based on the sensitivity of the optimal solution to changes in input parameters.
• ๐ฑ Sensitivity analysis can be applied to various aspects of a linear programming problem, such as changes in profitability, resource availability, or technology.

## Transcript

hello everybody and welcome to lesson 9 duality and post optimality analysis previously in lesson 8 we have discussed about one of the advantages of duality that is finding the solutions of the linear programming problem instead of using the primal problem we have used the dual to find out the solution or the optimal solutions of the primal problem... Read More

### Q: What is duality in linear programming and how does it help find solutions?

Duality in linear programming allows us to find solutions to the primal problem by solving its dual. The dual provides insight into the primal problem and the optimal solution can be obtained from the dual's solutions.

### Q: What is post-optimality analysis and when is it conducted?

Post-optimality analysis, also known as sensitivity analysis, examines changes after reaching the optimal solution of a linear programming problem. It is conducted once the optimal solution has been obtained.

### Q: What types of questions can be answered through post-optimality analysis?

Post-optimality analysis can answer questions about how changes in objective function coefficients or constraints affect the optimal solution. For example, it can determine the sensitivity of the optimal solution to changes in resource availability or profitability.

### Q: How is post-optimality analysis related to sensitivity analysis?

Post-optimality analysis is often referred to as sensitivity analysis. It helps determine the impact of changes in input parameters on the optimal solution without solving the entire linear programming problem again.

## Summary & Key Takeaways

• Duality in linear programming allows us to find optimal solutions by solving the dual problem instead of the primal problem.

• Post-optimality analysis, also known as sensitivity analysis, examines how changes in objective function coefficients or constraints affect the optimal solution.

• By conducting post-optimality analysis, we can answer questions about the sensitivity of the optimal solution to changes in input parameters and determine the range of changes that will not affect optimality.