Study guides

☆☆

Q: What is the feasible region in linear programming?

Write your answer...

Submit

Still have questions?

Related questions

Yes. There need not be a feasible region.

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.

Integer programming is a subset of linear programming where the feasible region is reduced to only the integer values that lie within it.

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.

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.

Yes. If the feasible region has a [constraint] line that is parallel to the objective function.

Each linear equation is a line that divides the coordinate plane into three regions: one "above" the line, one "below" and the line itself. For a linear inequality, the corresponding equality divides the plane into two, with the line itself belonging to one or the other region depending on the nature of the inequality. A system of linear inequalities may define a polygonal region (a simplex) that satisfies ALL the inequalities. This area, if it exists, is called the feasible region and comprises all possible solutions of the linear inequalities. In linear programming, there will be an objective function which will restrict the feasible region to a vertex or an edge of simplex. There may also be a further constraint - integer programming - where the solution must comprise integers. In this case, the feasible region will comprise all the integer grid-ponits with the simplex.

the phenomenon of obtaining a degenerate basic feasible solution in a linear programming problem known as degeneracy.

Yes. Although possible in real life, it is unlikely in school examples!

definition feasible region definition feasible region

In both cases the constraints are used to produce an n-dimensional simplex which represents the "feasible region". In the case of linear programming this is the feasible region. But that is not the case for integer programming since only those points within the region for which the variables are integer are feasible.The objective function is then used to find the maximum or minimum - as required. In the case of a linear programming problem, the solution must lie on one of the vertices (or along one line in 2-d, plane in 3-d etc) of the simplex and so is easy to find. In the case of integer programming, the optimal solution so found may contain one or more variables that are not integer and so it is necessary to examine all the points in the immediate neighbourhood and evaluate the objective function at each of these points. This last requirement makes integer programming solutions more difficult to find.

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?

i know that a feasible region, is the region which satisfies all the constraints but i don't know exactly why is the unshaded region regarded as a feasible region instead of the shaded region.

necessity of linear programming on organization.

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.

It would depend on the feasible region.

the feasible region is where two or more inequalities are shaded in the same place

the significance of duality theory of linear programming

Shinji Mizuno has written: 'Determination of optimal vertices from feasible solutions in unimodular linear programming' -- subject(s): Accessible book

Since there is no feasible region defined, there is no answer possible.

Yes they will. That is how the feasible region is defined.

essential attributes of linear programming models and its uses

A linear objective function and linear constraints.

The answer depends on what the feasible region is and on what operator is between 6x and 8y.

Integer programming is a method of mathematical programming that restricts some or all of the variables to integers. A subset of Integer programming is Linear programming. This is a form of mathematical programming which seeks to find the best outcome in such a way that the requirements are linear relationships.