A firm makes $x$ rings and $y$ chains, at most 24 items a day. A ring takes 1 hour, a chain 30 minutes, with 16 hours available. The time constraint is:

1. Each ring costs 1 hour, so $x$ rings use $x$ hours. 2. Each chain costs 30 minutes $=\tfrac12$ hour, so $y$ chains use $\tfrac12 y$ hours. 3. Total time cannot exceed the 16 hours available: $x+\tfrac12 y\le 16$. 4. The $\ge$ version misreads 'maximum number of hours available' as a floor rather than a ceiling. 5. The other two swap the coefficients, charging the ring half an hour and the chain a full hour. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 3: Linear Programming_