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Q: What is the feasible region in linear programming?

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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.

The answer depends on the feasible region and there is no information on which to determine that.

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The objective function and the constraints.

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?

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