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Is it possible for an linear programming model to have exact two optimal solutions?
Yes, but only if the solution must be integral.
There is a segment of a straight line joining the two optimal solutions. Since the two solutions are in the feasible region part of that line must lie inside the convex simplex. Therefore any solution on the straight line joining the two optimal solutions would also be an optimal solution.
What else can I help you with?
Can a linear programming problem have multiple optimal solutions?
When solving linear prog. problems, we base our solutions on assumptions.one of these assumptions is that there is only one optimal solution to the problem.so in short NO. BY HADI It is possible to have more than one optimal solution point in a linear programming model. This may occur when the objective function has the same slope as one its binding constraints.
Is it possible that there will be no feasible solutions in linear programming?
Yes. Although possible in real life, it is unlikely in school examples!
Why does Phase 1 in linear programming have alternative optimal solutions?
Phase 1 of linear programming aims to find a feasible solution to the problem by minimizing a "penalty" function, often involving artificial variables. If the feasible region is unbounded or if multiple ways exist to achieve the same minimum value for the penalty function, there can be alternative optimal solutions. This occurs when the objective function is parallel to a constraint boundary, allowing for multiple feasible points that yield the same objective value. Hence, the presence of alternative optimal solutions is tied to the geometry of the feasible region and the nature of the objective function.
What do you understand by linear programming problem?
1. What do you understand by Linear Programming Problem? What are the requirements of Linear Programming Problem? What are the basic assumptions of Linear Programming Problem?
Is it possible for a linear programming problem to have no solution?
Yes. There need not be a feasible region.
Can a linear programming problem have two optimal solutions?
No. However, a special subset of such problems: integer programming, can have two optimal solutions.
Can a linear programming problem have multiple optimal solutions?
When solving linear prog. problems, we base our solutions on assumptions.one of these assumptions is that there is only one optimal solution to the problem.so in short NO. BY HADI It is possible to have more than one optimal solution point in a linear programming model. This may occur when the objective function has the same slope as one its binding constraints.
Can a linear programming problem have exactly two optimal solutions?
Yes, a linear programming problem can have exactly two optimal solutions. This will be the case as long as only two decision variables are used within the problem.
Is it possible that there will be no feasible solutions in linear programming?
Yes. Although possible in real life, it is unlikely in school examples!
What has the author Shinji Mizuno written?
Shinji Mizuno has written: 'Determination of optimal vertices from feasible solutions in unimodular linear programming' -- subject(s): Accessible book
What has the author Toshinori Munakata written?
Toshinori Munakata has written: 'Matrices and linear programming with applications' -- subject(s): Linear programming, Matrices 'Solutions manual for Matrices and linear programming'
What is an optimization problem and how can it be effectively solved?
An optimization problem is a mathematical problem where the goal is to find the best solution from a set of possible solutions. It can be effectively solved by using mathematical techniques such as linear programming, dynamic programming, or heuristic algorithms. These methods help to systematically search for the optimal solution by considering various constraints and objectives.
Why does Phase 1 in linear programming have alternative optimal solutions?
Phase 1 of linear programming aims to find a feasible solution to the problem by minimizing a "penalty" function, often involving artificial variables. If the feasible region is unbounded or if multiple ways exist to achieve the same minimum value for the penalty function, there can be alternative optimal solutions. This occurs when the objective function is parallel to a constraint boundary, allowing for multiple feasible points that yield the same objective value. Hence, the presence of alternative optimal solutions is tied to the geometry of the feasible region and the nature of the objective function.
What is the strong duality proof for linear programming problems?
The strong duality proof for linear programming problems states that if a linear programming problem has a feasible solution, then its dual problem also has a feasible solution, and the optimal values of both problems are equal. This proof helps to show the relationship between the primal and dual problems in linear programming.
What is optimal solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
Is there no optimal solution in linear programming simplex method?
There usually is: particularly in examples that at set school or college level.
What is optimal feasible solution?
It is usually the answer in linear programming. The objective of linear programming is to find the optimum solution (maximum or minimum) of an objective function under a number of linear constraints. The constraints should generate a feasible region: a region in which all the constraints are satisfied. The optimal feasible solution is a solution that lies in this region and also optimises the obective function.
