Consider the Linear Programming Problem
Maximize \(z = x + y\)
Subject to the constraints \(x - y \le -1,\ x \ge y,\ x \ge 0, y \ge 0\)
Then which one of the following is TRUE?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → There is no solution
The first two constraints contradict each other:
\(x - y \le -1 \Rightarrow x \le y - 1 \lt y\)
\(x \ge y\)
No point can have both \(x \lt y\) and \(x \ge y\). So the feasible region is empty, and the problem has no solution. In particular, (1, 2), (7, 8) and the points of the line \(x - y = -1\) all have \(x \lt y\), so none of them is feasible.
NCERT (2026-27 edition):
Graphical Method of Solving Linear Programming Problems
