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    Question

    Which of the following statements is true about

    LPP?       
    A The feasible region is always a triangle Correct Answer Incorrect Answer
    B The objective function may attain extreme value at any point Correct Answer Incorrect Answer
    C LPP always has a unique solution Correct Answer Incorrect Answer
    D The feasible region is a convex polygon or unbounded region Correct Answer Incorrect Answer

    Solution

    In a Linear Programming Problem (LPP), the feasible region is the set of all possible solutions that satisfy the given constraints. The properties of the feasible region and behavior of the objective function are as follows:

    • The feasible region formed by a system of linear inequalities is always a convex set . It can either be a bounded convex polygon (like a triangle, quadrilateral, etc.) or an unbounded convex region.
    • The objective function in an LPP attains its maximum or minimum value only at the corner points (vertices) of the feasible region, not at any arbitrary point.
    • LPP may or may not have a unique solution. There can be multiple optimal solutions, a unique solution, no solution, or even an unbounded solution depending on the problem structure.
    • The feasible region is not necessarily a triangle; it depends on the number and nature of the constraints and can form various polygons.
    Thus, among the given options, the correct statement is:
    "The feasible region is a convex polygon or unbounded region."

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