Question

Which of the following is correct ?

• A. Every LPP admits an optimal solution.
• B. Every LPP admits a unique solution.
• C. The optimal value does not occur at a corner print of the feasible region only.
• D. If a LPP admits optimal solution at two points, then it has optimal solution at infinite number of points.

Answer 1

The Correct Option is D

The correct understanding of Linear Programming Problems (LPP) requires evaluating each statement:

1. Every LPP admits an optimal solution.
   This statement is false. An LPP may not have an optimal solution if it is unbounded or infeasible.
2. Every LPP admits a unique solution.
   This statement is false. An LPP can have multiple optimal solutions, especially along an edge of the feasible region.
3. The optimal value does not occur at a corner point of the feasible region only.
   This statement is false. In LPP, if an optimal solution exists, it has to occur at a vertex or along an edge formed by vertices of the feasible region.
4. If a LPP admits an optimal solution at two points, then it has an optimal solution at an infinite number of points.
   This statement is true. If two distinct points in the feasible region are optimal, then the entire line segment connecting these points is also optimal, implying infinite optimal solutions along the segment.

Thus, the correct answer is: If a LPP admits optimal solution at two points, then it has optimal solution at infinite number of points.