Match List-I with List-II (in each case, \(x \ge 0\) and \(y \ge 0\) also hold).
| List-I (Constraints) | List-II (Feasible region) | ||
| (A) | \(2x + 3y \le 12\) | (I) | No feasible point |
| (B) | \(x + 2y \ge 6\) | (II) | Unbounded region |
| (C) | \(x + y \le 2\), \(x + y \ge 5\) | (III) | Bounded region with 3 corner points |
| (D) | \(x \le 5\), \(y \le 2\) | (IV) | Bounded region with 4 corner points |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(II), (C)-(I), (D)-(IV)
(A) \(2x + 3y \le 12\)
This matches (III) Bounded region with 3 corner points.
The line meets the axes at (6, 0) and (0, 4). The region is the triangle with corners (0, 0), (6, 0) and (0, 4).
(B) \(x + 2y \ge 6\)
This matches (II) Unbounded region.
The region lies on the far side of the line x + 2y = 6 from the origin and goes on without end, for example through (0, t) for every \(t \ge 3\).
(C) \(x + y \le 2\), \(x + y \ge 5\)
This matches (I) No feasible point.
No number x + y can be at most 2 and at least 5 at the same time, so the feasible region is empty.
(D) \(x \le 5\), \(y \le 2\)
This matches (IV) Bounded region with 4 corner points.
The region is the rectangle with corners (0, 0), (5, 0), (5, 2) and (0, 2).