Answer: A maximum may not exist even if the corner point values suggest one, and must be checked separately.
- A A maximum tends to exist at a corner point in most cases, regardless of how unbounded the region is
- B A maximum may not exist even if the corner point values suggest one, and must be checked separately
- C Maximization becomes considerably harder to define clearly on an unbounded region
- D The feasible region would first need to be re-drawn artificially as a bounded shape
Correct answer: B. A maximum may not exist even if the corner point values suggest one, and must be checked separately
Explanation: On an unbounded feasible region, a value that looks like the maximum from corner points must be verified by checking whether the half-plane Z > that value has any point in common with the feasible region; if it does, no maximum exists.
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.