Question

The feasible region of an LPP is always:

• A. Circle
• B. Triangle only
• C. Convex polygon
• D. Straight line

Hint:

Since the feasible region is a convex polygon, the Corner Point Theorem states that the optimal solution (maximum or minimum value of the objective function) is guaranteed to occur at one of the corner points (vertices) of this polygon.

Answer 1

The Correct Option is C

Concept: In Linear Programming Problems (LPP), constraints are represented by linear inequalities. Graphically, each linear inequality defines a half-plane, which is a convex set. Key architectural geometric theorems dictate that:

• The intersection of any finite collection of convex sets is always a convex set.
• The geometric region formed by intersecting multiple linear half-planes creates a bounded or unbounded region enclosed by straight-line edges, known as a convex polygon (or a convex polyhedral set).

Step 1: Understanding the definition of a Convex Set.
A geometric set is defined as convex if, for any two points selected anywhere inside the region, the straight line segment connecting those two points lies completely within the boundaries of that region. Since all system constraint boundaries in a standard linear programming model are straight lines, the resulting feasible solution space cannot have indented contours or curved boundaries.

Step 2: Matching properties with options.
The intersecting boundary space forms vertices and edges, which matches the definition of a polygon. Because it must remain a convex structural set, the entire feasible region of an LPP is classified as a convex polygon.