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📐 Mathematics  ·  Linear Programming  ·  JEE

The common region that satisfies all the constraints is the:

Answer: feasible region.

  • A feasible region
  • B objective function
  • C corner point
  • D coordinate axis

Correct answer: A. feasible region

Explanation: The feasible region is the set of all points meeting every constraint.

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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