Zaymiey

📐 Mathematics  ·  Linear Programming  ·  JEE

If two corner points give the same optimal value of Z, then the optimum occurs at:

Answer: every point on the joining edge.

  • A every point on the joining edge
  • B only one single interior point
  • C the exact centre of the region
  • D no feasible point at all

Correct answer: A. every point on the joining edge

Explanation: When two vertices tie, every point on the segment joining them is also optimal.

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 →