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📐 Mathematics  ·  Linear Programming  ·  JEE

According to the fundamental theorem of linear programming, if an optimal value exists, where does it occur?

Answer: At a corner point of the feasible region.

  • A At the centroid of the feasible region
  • B At a corner point of the feasible region
  • C Anywhere inside the feasible region
  • D Outside the feasible region

Correct answer: B. At a corner point of the feasible region

Explanation: If an LPP has an optimal solution, it must occur at one of the corner points (vertices) 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.

Read the full Linear Programming notes →