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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.
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 does by 'optimal means' mean?
'optimal' means: best possible compromise solution to a problem, when there are several competing considerations, not all of which can be simulataneously maximized.
What is Difference between backtracking and branch and bound method?
Backtracking[1] It is used to find all possible solutions available to the problem.[2] It traverse tree by DFS(Depth First Search).[3] It realizes that it has made a bad choice & undoes the last choice by backing up.[4] It search the state space tree until it found a solution.[5] It involves feasibility function.Branch-and-Bound (BB)[1] It is used to solve optimization problem.[2] It may traverse the tree in any manner, DFS or BFS.[3] It realizes that it already has a better optimal solution that the pre-solution leads to so it abandons that pre-solution.[4] It completely searches the state space tree to get optimal solution.[5] It involves bounding function.
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.
What is the difference between feasible and optimal solution?
The optimal solution is the best feasible solution
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 the corner point solution method?
The corner point solution method is a technique used in linear programming to find the optimal solution by considering the intersection points of the constraints. It involves analyzing the extreme points or corner points of the feasible region to identify the optimal value of the objective function. This method is effective for problems with few variables and constraints.
State the difference between a feasible solution basic feasible solution and an optimal solution of a lpp?
the optimal solution is best of feasible solution.this is as simple as it seems
How can one determine the optimal pH level for a solution?
To determine the optimal pH level for a solution, you can use a pH meter or pH strips to measure the acidity or alkalinity of the solution. The optimal pH level will depend on the specific application or desired outcome of the solution. It is important to consider factors such as the properties of the substances in the solution and the intended use of the solution when determining the optimal pH level.
Why optimal solution is only at corner point?
feasible region gives a solution but not necessarily optimal . All the values more/better than optimal will lie beyond the feasible .So, there is a good chance that the optimal value will be on a corner point
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 difference between feasible solution and basic feasible solution?
optimal solution is the possible solution that we able to do something and feasible solution is the solution in which we can achieve best way of the solution
What is the recommended keyword density of lye solution in content for optimal effectiveness?
The recommended keyword density of lye solution in content for optimal effectiveness is generally around 1-2.
What is the similar property between dynamic programming and greedy approach?
Both are using Optimal substructure , that is if an optimal solution to the problem contains optimal solutions to the sub-problems
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.
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