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📐 Mathematics  ·  Linear Programming  ·  JEE

A furniture maker produces chairs (x) and tables (y). Each chair needs 2 hours of carpentry and 1 hour of finishing; each table needs 1 hour of carpentry and 3 hours of finishing. Only 40 carpentry hours and 60 finishing hours are available. If profit is Rs 30 per chair and Rs 60 per table, which is the correct constraint pair?

Answer: 2x + y <= 40 and x + 3y <= 60.

  • A 2x + y <= 40 and x + 3y <= 60
  • B x + 2y <= 40 and 3x + y <= 60
  • C 2x + y >= 40 and x + 3y >= 60
  • D x + y <= 40 and x + y <= 60

Correct answer: A. 2x + y <= 40 and x + 3y <= 60

Explanation: Carpentry: 2 hours per chair plus 1 hour per table, limited to 40 hours: 2x + y <= 40. Finishing: 1 hour per chair plus 3 hours per table, limited to 60 hours: x + 3y <= 60.

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 →