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WHAT IS HALF PLANE,CONVEX REGION,BOUNDED AND UNBOUNDED REGION,CORNER POINT IN LINEAR PROGRAMMING

WHAT IS HALF PLANE,CONVEX REGION,BOUNDED AND UNBOUNDED REGION,CORNER POINT IN LINEAR PROGRAMMING 

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Komal
askIITians Faculty 747 Points
8 years ago
A half-plane is a region on a co-ordinated plane for which an inequality in x, y or both is true.The idea of graphing a half-plane (such as 2x + 3y ≤ 6) is similar to graphing a line.
In linear programming problems with n variables, a necessary but not sufficient condition for the feasible set to be bounded is that the number of constraints be at least n + 1 (as illustrated by the above example).
If the feasible set is unbounded, there may or may not be an optimum, depending on the specifics of the objective function. For example, if the feasible region is defined by the constraint set {x ≥ 0, y ≥ 0}, then the problem of maximizing x + y has no optimum since any candidate solution can be improved upon by increasing x or y; yet if the problem is to minimize x + y, then there is an optimum (specifically at (x, y) = (0, 0)).

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