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CMA Intermediate · Operations Management and Strategic Management · Optimum Allocation of Resources - LPP

Sharma Furnitures makes tables (x) and chairs (y). A table needs 4 hours of carpentry and a chair needs 2 hours; 240 carpentry hours are available per week. Which constraint correctly represents this?

The constraint is 4x + 2y <= 240. Each table consumes 4 carpentry hours and each chair 2 hours, so total usage is 4x + 2y, and this cannot exceed the 240 hours available. Reversing the coefficients or the inequality sign would misstate the resource limit.

  1. A4x + 2y >= 240
  2. B2x + 4y <= 240
  3. C4x + 2y <= 240Correct
  4. D4x + 2y = 240 is the only permissible form and x,y can be negative

Explanation

Hours used = 4 per table times x plus 2 per chair times y = 4x + 2y. Availability is a maximum, so the sign is less than or equal. Option 2 swaps the coefficients, and option 1 reverses the inequality.

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