Answer: The LPP has multiple optimal solutions along the segment joining the two points.
- A There is a calculation error since two different points cannot give equal Z
- B The LPP has multiple optimal solutions along the segment joining the two points
- C The feasible region is empty
- D Neither point is actually a corner point
Correct answer: B. The LPP has multiple optimal solutions along the segment joining the two points
Explanation: Z(10,0)=300, Z(0,15)=300, both equal. This happens when the objective function's line is parallel to the boundary line joining these corners, giving infinitely many optimal solutions along that edge.
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.