The Library Printer Queue
A student council survey of 60 students at a polytechnic library found that 45 own a laptop, 30 own a tablet, and 12 own neither. The library has one shared printer that students can reach in two ways: (a) plug a laptop into the USB cable, or (b) send a print job over the campus Wi-Fi from a tablet using a print app. The print app only works on tablets, and the USB cable only works with laptops. During exam week the library expects 80 students to want to print, and each student prints an average of 3 pages. The printer handles 10 pages per minute, and the library is open for 6 hours. A staff member claims the printer will be overwhelmed because 'most students have two devices'.
1. Using the survey numbers, how many students own both a laptop and a tablet? Show your working and explain what this means for how students can print.
Read the worked answer
Total = 60. Neither = 12, so at least one device = 48.
Let both = x. Then:
- laptop only = 45 − x
- tablet only = 30 − x
- both = x
(45 − x) + (30 − x) + x = 48 75 − x = 48 x = 27
So 27 students own both, 18 own only a laptop, and 3 own only a tablet.
This matters for printing: the 27 who own both have two possible routes (USB via laptop, Wi-Fi via tablet), while the 18 laptop-only students must use USB and the 3 tablet-only students must use the app. The staff member's claim that 'most students have two devices' is actually correct (27 of 48 device owners, about 56%), but owning two devices makes printing easier, not harder, because it gives a fallback route.
2. The staff member says the printer will be overwhelmed. Test this claim using the exam-week estimate and state whether it is justified.
Read the worked answer
Demand: 80 students × 3 pages = 240 pages. Capacity: 10 pages/min × 60 min/hr × 6 hr = 3,600 pages in the open period.
Utilisation = 240 / 3,600 ≈ 6.7%.
Even if all 240 pages arrived in a single 30-minute burst, that is 240 pages at 10 pages/min = 24 minutes of printing, which still fits inside 30 minutes.
Conclusion: the claim is not justified on volume grounds. The printer has roughly 15× more capacity than the estimated demand. A better concern would be peak timing (everyone printing in the 20 minutes before an exam) or app/USB bottlenecks (only one cable, or Wi-Fi congestion), not total page volume.
3. Suppose the 3 tablet-only students cannot get the print app to install. Describe what information you would collect before deciding whether this is a serious problem, and why raw counts alone are not enough.
Read the worked answer
Raw counts say 3 out of 80 students (3.75%) are affected, which sounds trivial. But counts alone ignore:
- Timing: are those 3 printing the same critical document before the same exam?
- Substitutability: can they email the file to a friend, use a library PC, or print at a copy shop?
- Whether the survey figure is representative: the survey was of 60 students, not the 80 expected in exam week, so the tablet-only proportion may be different.
- Whether the app failure is universal or device-specific: one incompatible tablet model is a different problem from a campus-wide app outage.
I would collect: which tablet models fail, whether library PCs are available as an alternative, the deadline each affected student faces, and whether the failure rate in the survey sample matches the exam-week population. Only then can I judge severity. The decision is a judgement about impact and workarounds, not a count.