Question

A Linear Programming problem with a bounded feasible solution space will always have:

• A. Some basic feasible solutions but no optimal solution
• B. Some basic feasible solutions and at least one optimal solution
• C. No basic feasible solutions and no optimal solution
• D. No basic feasible solutions but at least one optimal solution

Hint:

When solving Linear Programming problems, always check the boundedness of the feasible region. If the region is unbounded, optimal solutions may not exist. Bounded feasible regions always contain basic feasible solutions at the vertices.

Answer 1

The Correct Option is B

In Linear Programming, when the feasible solution space is bounded, it means that the solution lies within a defined region of the feasible space. This bounded feasible region guarantees that there is at least one optimal solution. Furthermore, the bounded nature of the feasible region ensures that basic feasible solutions (which are the vertices of the feasible region) exist. Therefore, every Linear Programming problem with a bounded feasible region has at least one optimal solution, and some basic feasible solutions that correspond to the vertices of the region. Additionally, the optimal solution typically lies at one of these basic feasible solutions, which are also the corner points of the feasible region. This property is known as the Fundamental Theorem of Linear Programming.