Answer: fail to exist.
- A fail to exist
- B always exist
- C be exactly zero
- D be negative only
Correct answer: A. fail to exist
Explanation: On an unbounded region the objective can increase without limit, so a maximum may not exist.
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.