A machine can run for at most 12 hours a day. One unit of product P takes 30 minutes on the machine and one unit of product Q takes 45 minutes. If x units of P and y units of Q are made in a day, the constraint on machine time is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(2x + 3y \le 48\)
Both sides must be in the same unit. The machine time available is
\(12 \times 60 = 720\) minutes
The time used by x units of P and y units of Q cannot exceed this:
\(30x + 45y \le 720\)
Dividing by 15:
\(2x + 3y \le 48\)
Why the other options are incorrect
Option (1) \(30x + 45y \le 12\) — Incorrect. The left side is in minutes and the right side in hours.
Option (3) \(3x + 2y \le 48\) — Incorrect. The times are swapped: a unit of P takes the shorter time, 30 minutes.
Option (4) \(2x + 3y \ge 48\) — Incorrect. “At most” means the time used is less than or equal to the time available.