Answer: Every point on the line segment joining those two corners also gives the same maximum value.
- A There must be an error somewhere in the corner-point calculation that needs to be rechecked
- B Every point on the line segment joining those two corners also gives the same maximum value
- C The LPP has no solution because of the tie between the two corner points found
- D The feasible region is necessarily unbounded whenever such a tie between corners occurs
Correct answer: B. Every point on the line segment joining those two corners also gives the same maximum value
Explanation: When the objective function takes the same optimal value at two corner points, it takes that same value at every point on the segment joining them, giving infinitely many optimal solutions.
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.