Question

The value of objective function is maximum under linear constraints is

• A. at \((0,0)\)
• B. at the centre of feasible region
• C. at any point of feasible region
• D. at one of the corner points of the feasible region

Answer 1

The Correct Option is D

To determine where the value of an objective function is maximized under linear constraints, consider the structure of linear programming problems. A linear programming problem seeks to maximize or minimize a linear objective function, typically represented as \(Z = ax + by\), subject to a set of linear inequalities. The feasible region, which is the set of all possible solutions that satisfy these inequalities, is a convex polygon in a two-dimensional space.

Fundamental theorem of linear programming states that if there is an optimal solution, it occurs at a vertex, or corner point, of the feasible region. This is because the objective function will either max out or min out at one of the vertices, given the linear nature of the constraints and objective function.

Therefore, the maximum value of the objective function, under linear constraints, is attained at one of the corner points of the feasible region. This allows us to efficiently evaluate potential solutions by assessing only these vertex points.

Correct Answer: The value of the objective function is maximum at one of the corner points of the feasible region.