Consider the following statements about a linear programming problem:
(A) Every point on the boundary of the feasible region is a feasible solution.
(B) Any point outside the feasible region is called an infeasible solution.
(C) An optimal solution may be a point outside the feasible region, if it gives a better value of the objective function.
(D) The region other than the feasible region is called the optimal region.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (B) only
Points within and on the boundary of the feasible region are feasible solutions, and points outside it are infeasible solutions. An optimal solution is a point of the feasible region that gives the optimal value of the objective function.
So (A) and (B) are true, and (C) and (D) are false.
Checking the statements
(A) Every point on the boundary of the feasible region is a feasible solution. — Correct. Boundary points satisfy all the constraints.
(B) Any point outside the feasible region is called an infeasible solution. — Correct. It breaks at least one constraint.
(C) An optimal solution may be a point outside the feasible region, if it gives a better value of the objective function. — Incorrect. An optimal solution must be a feasible point.
(D) The region other than the feasible region is called the optimal region. — Incorrect. It is called the infeasible region.