Answer: 3x + y = 0.
- A 3x + 2y <= 12 and x + y <= 10, x,y >= 0
- B 3x + y >= 12 and x + 2y >= 10, x,y >= 0
- C x + 3y <= 12 and 2x + y <= 10, x,y >= 0
- D 3x + y <= 12 and x + 2y <= 10, x,y >= 0
Correct answer: D. 3x + y <= 12 and x + 2y <= 10, x,y >= 0
Explanation: Machine-hours: 3 per unit of A plus 1 per unit of B, limited to 12, giving 3x + y <= 12. Labour-hours: 1 per A plus 2 per B, limited to 10, giving x + 2y <= 10.
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.