For which of the following constraints does the region it describes NOT contain the origin?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2x + 5y \ge 10\)
Put \(x = 0, y = 0\) in each constraint. The origin lies in the region only if the inequality is true at (0, 0).
\(2(0) + 5(0) = 0\), and \(0 \ge 10\) is false
So the region \(2x + 5y \ge 10\) lies on the side of the line away from the origin.
Why the other options are incorrect
Option (1) \(3x + 2y \le 12\) — Incorrect. At (0, 0): \(0 \le 12\) is true.
Option (2) \(x - y \ge -3\) — Incorrect. At (0, 0): \(0 \ge -3\) is true.
Option (4) \(x - 4y \le 4\) — Incorrect. At (0, 0): \(0 \le 4\) is true.