Match List-I with List-II (in each case, \(x \ge 0\) and \(y \ge 0\) also hold).
| List-I | List-II | ||
|---|---|---|---|
| Constraints | Feasible region | ||
| (A) | \(x + y \le 4\), \(x + y \ge 4\) | (I) | No feasible point |
| (B) | \(x + y \le 3\), \(x \ge 3\) | (II) | A line segment |
| (C) | \(x + 2y \le 4\), \(x \ge 5\) | (III) | A single point |
| (D) | \(x - y \le 1\), \(y \ge 2\) | (IV) | An unbounded region |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(III), (C)-(I), (D)-(IV)
(A) \(x + y \le 4\), \(x + y \ge 4\)
Together they give \(x + y = 4\), with \(x, y \ge 0\)
The feasible points are those of the segment joining (4, 0) and (0, 4). This matches (II) a line segment.
(B) \(x + y \le 3\), \(x \ge 3\)
\(y \le 3 - x \le 0\), and \(y \ge 0\), so \(y = 0\) and \(x = 3\)
Only (3, 0) is feasible. This matches (III) a single point.
(C) \(x + 2y \le 4\), \(x \ge 5\)
\(x + 2y \ge 5 + 0 = 5 \gt 4\)
No point satisfies both. This matches (I) no feasible point.
(D) \(x - y \le 1\), \(y \ge 2\)
Points (t, t) with \(t \ge 2\) satisfy both, for t as large as we like
This matches (IV) an unbounded region.