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📐 Mathematics  ·  Linear Programming  ·  JEE

A manufacturing problem in linear programming typically aims to:

Answer: Maximize profit subject to limited resources.

  • A Minimize the number of products
  • B Maximize profit subject to limited resources
  • C Maximize the use of raw material regardless of cost
  • D Minimize the number of decision variables

Correct answer: B. Maximize profit subject to limited resources

Explanation: A manufacturing problem usually maximizes profit (the objective function) subject to constraints like limited labour hours, machine hours, or raw material.

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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