Which of the following are correct about the linear programming problem (LPP)?
(A) The objective function is always linear.
(B) A corner point of a feasible region is a point in the region which is the intersection of two boundary lines.
(C) The common region determined by all the linear constraints of a LPP is called the feasible region.
(D) If an LPP admits optimal solution at two points then its optimal values occurs at an infinite number of points.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B), (C) and (D)
All four statements are standard facts about a linear programming problem.
Checking the statements
(A) The objective function is always linear. — Correct. In an LPP the objective function is a linear function \(Z = ax + by\).
(B) A corner point of a feasible region is a point in the region which is the intersection of two boundary lines. — Correct. This is the definition of a corner point.
(C) The common region determined by all the linear constraints of a LPP is called the feasible region. — Correct. This is the definition of the feasible region.
(D) If an LPP admits optimal solution at two points then its optimal values occurs at an infinite number of points. — Correct. If Z has the same optimal value at two points, it has that value at every point of the segment joining them, and a segment has infinitely many points.