Packing-Shop Staffing and the 26-Hour Window
A small packing shop has a rush order for 1,056 units. Three workers are assigned: A packs 24 units per hour, B packs 18 per hour, and C packs 12 per hour. For the first 4 hours, all three work together. Then C is reassigned, and A and B continue at their steady rates. The customer's delivery window is 26 hours from the start, and the shop wants at least a 2-hour buffer. Breaks are already included in the rates, so no additional downtime needs to be added. The supervisor wants to know whether the order will make the window, how much time would be saved if C stayed, and what extra capacity would be needed to finish in 22 hours instead.
1. How long will the order take under the actual staffing plan, and does it meet the 26-hour window with a 2-hour buffer?
Read the worked answer
First find the combined rate for the first 4 hours:
- A + B + C = 24 + 18 + 12 = 54 units/hour.
- Work completed in 4 hours = 54 × 4 = 216 units.
- Remaining work = 1,056 − 216 = 840 units.
After C leaves, the rate is A + B = 24 + 18 = 42 units/hour.
- Time for remaining work = 840 ÷ 42 = 20 hours.
- Total time = 4 + 20 = 24 hours.
The window is 26 hours, so the finish is 2 hours early. That meets the requested 2-hour buffer exactly, with no extra cushion.
2. If C could stay for the entire order, how much time would be saved?
Read the worked answer
With all three workers for the whole order, the rate is 54 units/hour.
- Total time = 1,056 ÷ 54 = 19.555… hours.
- Convert the decimal part: 0.555… × 60 ≈ 33 minutes.
- So the time would be about 19 hours 33 minutes.
The actual plan takes 24 hours. The saving is:
- 24 h − 19 h 33 min = 4 h 27 min.
So keeping C would save roughly 4.5 hours, but the order already fits the window without that change.
3. To finish in 22 hours with C leaving after hour 4, what combined additional packing rate is required after hour 4?
Read the worked answer
The first 4 hours still produce 216 units, leaving 840 units.
If the total time must be 22 hours, the time after hour 4 is:
- 22 − 4 = 18 hours.
The required rate for A and B together is:
- 840 ÷ 18 = 46.67 units/hour.
A and B currently provide 42 units/hour, so the shortfall is:
- 46.67 − 42 = 4.67 units/hour.
They need about 4.7 additional units per hour of combined capacity after hour 4, for example a helper who can pack at least 5 units/hour.