The Overloaded School Canteen
A school canteen serves 600 students in a single 40-minute lunch break. There are three serving counters, each able to serve one student every 20 seconds. Students arrive in a burst: about 70% arrive in the first 10 minutes, the rest spread evenly across the remaining 30 minutes. The canteen manager notices long queues and complaints, and proposes adding a fourth counter, which would cost the school an extra 1,500 currency units per month. A student council survey found that 45% of students would rather eat outside the canteen if given permission, and the school has a small outdoor seating area for 80 students. The principal wants a decision before the next term.
1. Calculate whether the three existing counters can serve all arrivals within the 40-minute break, and identify the bottleneck.
Read the worked answer
Total capacity: 3 counters × (40 min × 60 s ÷ 20 s per student) = 3 × 120 = 360 students served in the full break.
Demand: 600 students. So even with perfect flow, three counters serve only 360, leaving 240 unserved.
Burst analysis: In the first 10 minutes, 70% of 600 = 420 students arrive. Capacity in 10 minutes = 3 × (600 ÷ 20) = 3 × 30 = 90 students. The queue after 10 minutes is 420 − 90 = 330 students.
Remaining 30 minutes: arrivals = 180, capacity = 3 × 90 = 270. Net drain = 270 − 180 = 90 per 30 min, so the queue only shrinks from 330 to 240 by the end.
Bottleneck: serving throughput, not seating. The counters are the constraint, and the burst timing makes it worse than the average suggests.
2. Compare adding a fourth counter against allowing outdoor eating, using the numbers. Which do you recommend and why?
Read the worked answer
Fourth counter: capacity becomes 4 × 120 = 480 in the break, still short of 600 by 120. Cost 1,500/month. It helps but does not clear demand.
Outdoor option: 80 seats absorb 80 students, reducing canteen demand to 520. Still above 360 capacity, so alone it also fails.
Combined: 4 counters (480) + 80 outdoor = 560, still 40 short. So neither single fix nor the obvious combination fully solves it.
Recommendation: Do not buy the counter alone. A cheaper mix: stagger arrivals (e.g., two sittings) so the 70% burst is split, plus open the 80 outdoor seats. Staggering alone can cut peak queue substantially because capacity per 40-minute window is unchanged but the burst is halved. If budget allows, the counter plus staggering plus outdoor seats is the robust answer. The judgement point: match the fix to the bottleneck (throughput and burst timing), not to the symptom (queues).
3. The survey says 45% prefer eating outside. Does that justify relying on outdoor seating? Explain the reasoning trap.
Read the worked answer
No. 45% of 600 = 270 students say they prefer outside, but only 80 can be seated there. Stated preference is not capacity. The survey measures desire, not behaviour under constraints (weather, supervision, time).
Reasoning trap: treating a preference percentage as if it were an available solution. The real limit is 80 seats, so the outdoor option removes at most 80 from the canteen queue regardless of the 45% figure.
A defensible answer notes both: the 45% shows demand exists and may justify expanding outdoor seating later, but for this term the binding number is 80. Decision-makers should convert preferences into physical capacity before counting them as relief.