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📐 Mathematics  ·  Linear Programming  ·  JEE

In an LPP, what does a corner point represent geometrically?

Answer: A point where two boundary constraint lines (or a boundary line and an axis) intersect.

  • A The centroid, or geometric centre, of the entire bounded feasible region shape itself
  • B A point where two boundary constraint lines (or a boundary line and an axis) intersect
  • C A randomly chosen point lying somewhere inside the broader feasible region
  • D The exact midpoint of the line representing the objective function itself

Correct answer: B. A point where two boundary constraint lines (or a boundary line and an axis) intersect

Explanation: Corner points (vertices) occur where two boundary lines of the feasible region meet, including intersections with the coordinate axes.

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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