Answer: A minimum can exist at a corner point, since the region is bounded below-left even though unbounded elsewhere.
- A No minimum tends to exist once the feasible region is unbounded in most of the relevant directions here
- B A minimum can exist at a corner point, since the region is bounded below-left even though unbounded elsewhere
- C A maximum typically exists at one of the corner points instead, regardless of unboundedness elsewhere
- D The objective function becomes largely undefined whenever the feasible region is unbounded like this
Correct answer: B. A minimum can exist at a corner point, since the region is bounded below-left even though unbounded elsewhere
Explanation: Even though the feasible region is unbounded in some directions, a minimum can still exist at a corner point if the region is closed off in the direction that would decrease the objective function further.
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.