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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 multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
What is simplex method of linear programming?
The simplex method is an algorithm used for solving linear programming problems, which aim to maximize or minimize a linear objective function subject to linear constraints. It operates on a feasible region defined by these constraints, moving along the edges of the feasible polytope to find the optimal vertex. The method iteratively improves the solution by pivoting between basic feasible solutions until no further improvements can be made. It's widely used due to its efficiency and effectiveness in handling large-scale linear optimization problems.
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 simplex method in linear programming?
The simplex method is an algorithm used to solve linear programming problems by optimizing a linear objective function, subject to linear equality and inequality constraints. It operates on feasible solutions at the vertices of the feasible region defined by the constraints, iteratively moving towards the optimal solution by pivoting between these vertices. The method is efficient for solving large-scale linear programs and is widely used in various fields, including economics, engineering, and operations research.
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 multiple solutions?
Yes. If the feasible region has a [constraint] line that is parallel to 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 simplex method of linear programming?
The simplex method is an algorithm used for solving linear programming problems, which aim to maximize or minimize a linear objective function subject to linear constraints. It operates on a feasible region defined by these constraints, moving along the edges of the feasible polytope to find the optimal vertex. The method iteratively improves the solution by pivoting between basic feasible solutions until no further improvements can be made. It's widely used due to its efficiency and effectiveness in handling large-scale linear optimization problems.
Distinguish between integer programming problem and linear programming problem?
Integer programming is a subset of linear programming where the feasible region is reduced to only the integer values that lie within it.
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
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 feasible region of a linear programming problem?
After graphing the equations for the linear programming problem, the graph will have some intersecting lines forming some polygon. This polygon (triangle, rectangle, parallelogram, quadrilateral, etc) is the feasible region.
What is simplex method in linear programming?
The simplex method is an algorithm used to solve linear programming problems by optimizing a linear objective function, subject to linear equality and inequality constraints. It operates on feasible solutions at the vertices of the feasible region defined by the constraints, iteratively moving towards the optimal solution by pivoting between these vertices. The method is efficient for solving large-scale linear programs and is widely used in various fields, including economics, engineering, and operations research.
How do you solve linear programming with no feasible region?
When a linear programming problem has no feasible region, it typically indicates that the constraints are contradictory, making it impossible to find a solution that satisfies all conditions. To address this, first, review the constraints for inconsistencies or errors. If contradictions are found, reformulate the problem by adjusting constraints to create a feasible region. If adjustments are not possible, it may be necessary to reconsider the problem's formulation or objectives.
Non-degenerate basic feasible solution?
A non-degenerate basic feasible solution in linear programming is one where at least one of the basic variables is strictly positive. In contrast to degenerate solutions where basic variables might be zero, non-degenerate solutions can help optimize algorithms as they ensure progress in the search for the optimal solution.
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.
