A feasible solution in a linear programming problem (LPP):
(A) Must satisfy all the problem’s constraints simultaneously
(B) Need not satisfy all the constraints, only some of them
(C) Must be a corner point in the feasible region
(D) May or may not optimise the value of the objective function
(E) Must be greater than or equal to zero
Choose the correct answer from the options given below :

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Correct option is A

Correct Answer: 1. (A), (D), (E) only
Explanation:

• Statement (A) is Correct: By definition, a feasible solution is any set of values for the decision variables that satisfies all the structural constraints and non-negativity restrictions of the problem simultaneously.
  
• Statement (D) is Correct: A feasible solution is merely a valid candidate. It may or may not optimise (maximize or minimize) the objective function. The specific feasible solution that optimizes the function is called the optimal solution.
  
• Statement (E) is Correct: In the standard formulation of a Linear Programming Problem (LPP), the decision variables are subject to non-negativity constraints, meaning they must be greater than or equal to zero ($$x \ge 0$$​).

Information Booster:

• Feasible Region: The collection of all feasible solutions forms a convex set known as the feasible region.
  
• Basic Feasible Solution (BFS): A feasible solution that corresponds to a corner point (vertex) of the feasible region.
  
• Fundamental Theorem of LPP: If an optimal solution exists, it will occur at one of the corner points (extreme points) of the feasible region.
  
• Infeasible Solution: Any solution that violates at least one constraint.
  

Additional Information:

• Statement (B) : This is Incorrect. If a solution violates even a single constraint, it falls outside the feasible region and is termed an infeasible solution.
  
• Statement (C) : This is Incorrect. This defines a Basic Feasible Solution. A general feasible solution can be any point inside or on the boundary of the feasible region, not necessarily a corner.