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📐 Mathematics  ·  Linear Programming  ·  JEE

The requirement that the variables be greater than or equal to zero is the ___ restriction:

Answer: non-negativity.

  • A non-negativity
  • B positivity-only
  • C equality
  • D boundary

Correct answer: A. non-negativity

Explanation: The non-negativity restrictions x ≥ 0, y ≥ 0 keep the solution in the first quadrant.

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 →