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📐 Mathematics  ·  Linear Programming  ·  JEE

If the optimal value of an LPP occurs at two adjacent corner points, then the problem has:

Answer: infinitely many optimal solutions.

  • A a unique solution
  • B no solution
  • C infinitely many optimal solutions
  • D an unbounded solution

Correct answer: C. infinitely many optimal solutions

Explanation: The entire edge joining those corners is optimal, giving infinitely many solutions.

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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