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.
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.