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📐 Mathematics  ·  Linear Programming  ·  JEE

By the corner-point theorem, the optimum of the objective function is attained at a:

Answer: vertex of the feasible region.

  • A vertex of the feasible region
  • B centre of the region
  • C point outside the region
  • D curved boundary point

Correct answer: A. vertex of the feasible region

Explanation: The maximum or minimum, if it exists, occurs at a vertex (corner point) of the feasible region.

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.

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