Answer: 2x + y >= 8 and x + 2y >= 11.
- A 2x + y >= 8 and x + 2y >= 11
- B 2x + y <= 8 and x + 2y <= 11
- C x + 2y >= 8 and 2x + y >= 11
- D 2x + y >= 11 and x + 2y >= 8
Correct answer: A. 2x + y >= 8 and x + 2y >= 11
Explanation: Vitamin A requirement: 2 units from Food 1 plus 1 unit from Food 2 per item, total at least 8: 2x + y >= 8. Vitamin B: 1 unit from Food 1 plus 2 units from Food 2, total at least 11: x + 2y >= 11.
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.