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.
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.
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?
Yes. There need not be a feasible region.
Yes. If the feasible region has a [constraint] line that is parallel to the objective function.
Shinji Mizuno has written: 'Determination of optimal vertices from feasible solutions in unimodular linear programming' -- subject(s): Accessible book
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.
Integer programming is a subset of linear programming where the feasible region is reduced to only the integer values that lie within it.
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.
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.
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.
A feasible region is, in a constrained optimization problem, the set of solutions satisfying all equalities and/or inequalities. On the other hand a linear programming is a constrained optimization problem in which both the objective function and the constraints are linear, therefore a feasible region on a linear programming problem is the set of solutions of the a linear problem. Many algorithms had been designed to successfully attain feasibility at the same time as resolving the problem, e.g. reaching its minimum. Perhaps one of the most famous and extensively utilized is the Simplex Method who travels from one extremal point to another, which happens to be the possible extrema given the convex nature of the problem, by maintaining a fixed number of components to zero, called basic variables. Then, the algorithm arrives to a global minimum generally in polinomial time even if its worst possible case has already been proved to be exponencial, see Klee-Minty's cube.