Yes. Although possible in real life, it is unlikely in school examples!
Yes. There need not be a feasible region.
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
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.
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.
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.
Yes. There need not be a feasible region.
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
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.
Integer programming is a subset of linear programming where the feasible region is reduced to only the integer values that lie within it.
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.
Shinji Mizuno has written: 'Determination of optimal vertices from feasible solutions in unimodular linear programming' -- subject(s): Accessible book
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.
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.
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.
Toshinori Munakata has written: 'Matrices and linear programming with applications' -- subject(s): Linear programming, Matrices 'Solutions manual for Matrices and linear programming'
the phenomenon of obtaining a degenerate basic feasible solution in a linear programming problem known as degeneracy.
No. However, a special subset of such problems: integer programming, can have two optimal solutions.