Food Bank Packing Target
A food bank packs identical parcels at two sites. Site A has five volunteers who each pack 12 parcels per hour for the first three hours; after that, one volunteer leaves and the remaining four slow to 9 parcels per hour because of fatigue. Site B has three volunteers who each pack 10 parcels per hour throughout, but they lose the first 30 minutes of the five-hour window waiting for a delivery. A partner agency has requested 400 parcels by the end of the window. Parcels cannot be moved between sites during the window, but finished parcels at both sites count toward the total. A Site A volunteer claims the two sites will exceed the request by about 30 parcels.
1. Calculate the total number of parcels the two sites will pack in the five-hour window. State whether the volunteer's claim is correct.
Read the worked answer
Site A: first 3 hours = 5 × 12 × 3 = 180 parcels. Final 2 hours = 4 × 9 × 2 = 72. Site A total = 252. Site B: available time = 5 h − 0.5 h = 4.5 h; output = 3 × 10 × 4.5 = 135. Combined = 387. The request is 400, so the sites fall short by 13, not exceed by 30. The volunteer's claim is wrong in both direction and magnitude: the gap between claim and reality is 43 parcels. The error probably comes from ignoring the volunteer who leaves and from treating Site B's lost 30 minutes as negligible. Check: if the leaver had stayed, Site A would have produced 5 × 9 × 2 = 90 in the last two hours, adding 18, for a total of 405 - which would exceed by 5, still not 30. So even the most generous assumption does not rescue the claim.
2. If the shortfall is to be closed only in the final two hours at Site A, what is the smallest whole number of additional volunteers needed, assuming each added volunteer packs at the Site A fatigue rate?
Read the worked answer
Shortfall is 13 parcels. At the fatigue rate, one volunteer produces 9 parcels per hour, so the requirement is 13 ÷ 9 ≈ 1.44 volunteer-hours. Because volunteers work in whole-person shifts, one additional volunteer working the full final two hours produces 18 parcels, which closes the gap with 5 to spare. If the site can only add people for one-hour blocks, two volunteers for the final hour also produce 18. The smallest number of additional volunteers is therefore one, provided that person can work both remaining hours; otherwise two. The answer depends on the shift granularity, which should be stated rather than assumed.
3. Identify one assumption in the calculation that, if false, would change the conclusion, and quantify its effect.
Read the worked answer
One key assumption is that Site B's three volunteers maintain 10 parcels per hour for the full 4.5 hours. If fatigue affects them as it affects Site A, their output falls and the shortfall grows. Another is that the 30-minute delivery delay is the only lost time; a second delay would reduce Site B by 15 parcels per half hour (3 × 10 × 0.5), turning a 13-parcel shortfall into 28. A third is that all packed parcels meet quality standards; if 5% are rejected, 387 becomes about 368. The estimate is a planning figure, not a guarantee, so the coordinator should build in a buffer or confirm rates with a short trial.