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📐 Mathematics  ·  Linear Programming  ·  JEE

Linear programming is a method for finding the ___ value of a linear function subject to constraints:

Answer: the optimal (best) value.

  • A the optimal (best) value
  • B just the average value
  • C just the median value
  • D a purely random value

Correct answer: A. the optimal (best) value

Explanation: An LPP finds the optimal (maximum or minimum) value of a linear objective function.

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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