Dock Dispatch Cutoff
You supervise the outgoing dock at a processing facility. Tonight's hub truck departs at 22:00. Three containers are already staged: A holds 4,180 pieces, B holds 2,965, and C holds 3,875. At 20:40 a late collection arrives with 2,340 more pieces. The truck can carry up to 14,000 pieces; any excess would require a second truck costing $310 and departing at 23:15. Sorting the late collection takes 12 minutes per 500 pieces, rounding up to the next full 500. Loading the truck takes 25 minutes after all sorting is finished. The drive to the hub takes 70 minutes, and the hub will not accept arrivals after 23:30.
1. How many pieces are available for the 22:00 truck, and does the load exceed capacity? Show your arithmetic.
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Staged total: 4,180 + 2,965 + 3,875 = 11,020 pieces.
Add the late collection: 11,020 + 2,340 = 13,360 pieces.
Capacity is 14,000, so 13,360 is under capacity by 14,000 − 13,360 = 640 pieces. No second truck is needed on volume grounds.
2. Using the sorting and loading times, determine whether the late collection can make the 22:00 departure. What is the earliest the truck can leave, and does that meet the hub cutoff?
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Sort blocks: 2,340 ÷ 500 = 4.68, which rounds up to 5 blocks.
Sorting time: 5 × 12 = 60 minutes, so sorting finishes at 20:40 + 60 = 21:40.
Loading then runs 21:40 to 22:05 (25 minutes).
The truck misses 22:00 by 5 minutes. Check the cutoff: 22:05 + 70 minutes = 23:15 arrival, which is before 23:30, so a 22:05 departure still meets the hub cutoff.
3. A coworker proposes holding the late mail for the 23:15 second truck to protect the 22:00 departure. Using the numbers, recommend a course of action and state the main assumption behind your recommendation.
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Recommendation: delay the single truck to 22:05 and take all 13,360 pieces.
Reasoning:
- All mail fits on one truck (13,360 < 14,000).
- A 22:05 departure arrives at 23:15, inside the 23:30 cutoff, with 15 minutes of slack.
- Holding 2,340 pieces for a second truck costs $310 and splits the load for no capacity benefit.
Main assumption: the 70-minute drive time and 23:30 cutoff are reliable tonight. If road conditions add more than about 15 minutes, the 22:05 plan fails the cutoff and the second-truck option must be reconsidered.