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📐 Mathematics  ·  Linear Programming  ·  JEE

The set of all feasible solutions of a two-variable LPP forms a:

Answer: convex polygon.

  • A convex polygon
  • B circle
  • C parabola
  • D single straight line

Correct answer: A. convex polygon

Explanation: The feasible region bounded by linear constraints is a convex polygon.

Feasible Region and Corner PointsxyOABCfeasible regionZ = ax+by is evaluated ONLY at corners O, A, B, C - the optimum is always at one of these

The feasible region (shaded) is bounded by the constraint lines; the fundamental theorem of LPP guarantees the optimal value of the objective function occurs at one of the corner points (O, A, B, C), so only these need to be checked, not the entire region.

Concept context

Optimizing a linear objective function subject to linear constraints using the graphical corner point method.

Read the full Linear Programming notes →