Consider the following statements
I. If the feasible region of an LPP is undbounded then maximum or minimum value of the obJective function Z = ax + by may or may not exist .
II. Maximum value of the objective function Z = ax + by in an LPP always occurs at only one corner point of the feasible region.
Ill. In an LPP, the minimum value of the objective function Z = ax + by is always 0, if origin is one of the corner point of the feasible region.
IV. In an LPP, the maximum value of the objective function Z = ax + by is always finite.
Which of the following statements are true?

Options

A. I and IV
B. II and III
C. I and III
D. II and IV

Answer

A

Explanation

Maximum value of the objective function Z =ax+ by in an LPP may occur at more than one corner points.
` therefore ` Statement II is false Also, in an LPP, since both x and y cannot be zero simultaneously. `therefore ` Minimum value of the objective function Z = ax + by cannot be 0, if origin is one of the corner point of the feasible solution.
`therefore ` Statement Ill is false.
If the feasible region for LPP is unbounded, then maximum or minimum of the objective function Z = ax + by may or may not exist, statement I is correct.
Also, in an LPP the maximum value of the objective function Z = ax + by is always finite.