The feasible region of a linear programming problem is bounded. The corresponding objective function is \(Z=3x-4y\). The objective function attains
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → both maximum and minimum value of Z attained in the feasible region
By the fundamental theorem of linear programming, when the feasible region is bounded, the objective function \(Z = ax + by\) has both a maximum and a minimum value on it, and each occurs at a corner point of the region.
This holds for every linear objective function, so it holds for \(Z = 3x - 4y\). Only for an unbounded region may the maximum or the minimum fail to exist.
CBSE Applied Mathematics (Class XII):
Linear Programming
