Linear programming duality

In summary, linear programming duality is a mathematical concept that relates a linear programming problem to a dual problem. The dual problem has the same number of variables but a different objective function and constraints. The primal and dual problems are closely related and can be used to find optimal solutions for each other. This concept is useful for gaining a deeper understanding of linear programming problems and has applications in various fields, such as economics and engineering.
  • #1
theakdad
211
0
I have an hour to solve this problem.

I have calculated the duality of linear problem. My question is,whats the range i can change some values,so the optimal solution stay as it is?
Is there an easy way to calculate it?
Thanks to all!
 
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  • #2
Unfortunately, there is no easy way to calculate the range of values that can be changed while maintaining the optimal solution. This requires solving a series of related optimization problems and comparing the solutions. Depending on how complex your linear problem is, it could take significantly longer than an hour to solve.
 

FAQ: Linear programming duality

What is linear programming duality?

Linear programming duality is a mathematical concept that states that for every linear programming problem, there exists a dual problem that is closely related to it.

How does linear programming duality work?

Linear programming duality works by taking a linear programming problem and creating a related problem known as the dual problem. The dual problem has the same number of variables as the original problem but has a different objective function and constraints.

What is the relationship between the primal and dual problems in linear programming duality?

The primal and dual problems in linear programming duality are closely related and are said to be dual to each other. This means that the solution to one problem can be used to find the solution to the other problem, and the optimal values of the objective functions in both problems will be equal.

How is linear programming duality useful?

Linear programming duality is useful because it allows for a deeper understanding of a linear programming problem by providing a different perspective. It also allows for the creation of efficient algorithms for solving linear programming problems.

What are the applications of linear programming duality?

Linear programming duality has various applications in fields such as economics, operations research, and engineering. It can be used to solve optimization problems, find optimal solutions to resource allocation problems, and analyze the efficiency of different systems.

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