For the linear programming problem (LPP),
Maximize \(Z = 7x+9y\), subject to constraints,
\(x-y \le -1,\ -x + y \le 0,\quad x, y \ge 0.\)
Which of the following is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → No feasible region exists.
Rewriting the first two constraints:
\(x - y \le -1 \Rightarrow y \ge x + 1\)
\(-x + y \le 0 \Rightarrow y \le x\)
Both together need \(x + 1 \le y \le x\), that is, \(x + 1 \le x\), which is never true. The two half-planes lie on opposite sides of the parallel lines y = x and y = x + 1, so no point satisfies both, and no feasible region exists.
Options (1), (2) and (3) all assume a feasible region; for example, the point (1, 1) breaks \(y \ge x + 1\).