A school wants to buy x desks and y chairs. A desk costs Rs. 3000 and a chair costs Rs. 1000. The school can spend at most Rs. 60000, and the room can hold at most 30 pieces of furniture. Besides \(x \ge 0\), \(y \ge 0\), the constraints are
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(3x + y \le 60\), \(x + y \le 30\)
Cost of x desks and y chairs (in Rs.):
\(3000x + 1000y \le 60000\)
Dividing by 1000:
\(3x + y \le 60\)
The room holds at most 30 pieces:
\(x + y \le 30\)
“At most” gives ≤ in both constraints.
Why the other options are incorrect
Option (1) \(x + 3y \le 60\), \(x + y \le 30\) — Incorrect. It puts the price Rs. 3000 on the chairs instead of the desks.
Option (2) \(3x + y \ge 60\), \(x + y \le 30\) — Incorrect. “At most Rs. 60000” means the cost cannot go above 60000, so the sign is ≤, not ≥.
Option (4) \(3x + y \le 60\), \(x + y \ge 30\) — Incorrect. The room holds at most 30 pieces, so the number of pieces must be ≤ 30, not ≥ 30.