Question

Which of the following statements is true ?
A. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.
B. Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
C. In a LPP, the minimum value of the objective function Z = ax + by (a, b > 0) is always 0 if origin is one of the corner points of feasible region.
D. In a LPP the max value of the objective function Z = ax + by is always finite.
Choose the correct answer from the options given below :

• A. B, C and D only
• B. A and C only
• C. A, B and C only
• D. C and D only

Answer 1

The Correct Option is B

The problem involves evaluating the truthfulness of statements regarding Linear Programming Problems (LPP). Let's analyze each statement:

A. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.

Explanation: In an unbounded feasible region, if the level curve of the objective function points outward, the objective function may increase or decrease indefinitely, indicating that the maximum or minimum may not exist. Therefore, statement A is true.

B. Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.

Explanation: The maximum value of a linear objective function in a bounded feasible region occurs at one or more corner points; however, it is not restricted to only one point if multiple points give the same maximum value. Hence, statement B is false.

C. In a LPP, the minimum value of the objective function Z = ax + by (a, b > 0) is always 0 if origin is one of the corner points of the feasible region.

Explanation: If the objective function can reach the origin (i.e., where x = 0 and y = 0) in its feasible region and a, b > 0, the value of Z = 0, the minimum value is 0. Therefore, statement C is true.

D. In a LPP the max value of the objective function Z = ax + by is always finite.

Explanation: In unbounded feasible regions, the maximum value of a linear objective function may not be finite as it can increase indefinitely, thus making statement D false.

Therefore, correct statements are A and C. Answer: A and C only.