The Overtime Budget Squeeze
A warehouse crew of 6 workers must finish a 4,200-unit packing order in 5 working days. Each worker packs at a steady rate of 12 units per hour during a standard 8-hour shift, and the crew has already logged 3 full days at that rate. On the morning of day 4, a supervisor reports that 1,260 units remain. Overtime is paid at 1.5 times the regular hourly rate of $18, but the overtime budget for this order is capped at $1,000. The manager wants to know whether the remaining units can be finished on time using only scheduled hours, and if not, whether the overtime cap allows the crew to close the gap.
1. Determine whether the remaining 1,260 units can be completed within the two remaining standard workdays without overtime. Show your rate calculation.
Read the worked answer
Daily crew capacity (standard hours):
- 6 workers × 12 units/hour × 8 hours = 576 units per day.
Capacity over the 2 remaining days:
- 576 × 2 = 1,152 units.
Compare to remaining work:
- 1,152 < 1,260, so the crew is short by 108 units.
Conclusion: No - standard hours alone leave 108 units unfinished. Overtime is required.
2. If the crew uses overtime to cover the shortfall, calculate the minimum overtime cost and decide whether it fits the $1,000 cap.
Read the worked answer
Shortfall: 1,260 − 1,152 = 108 units.
Crew overtime rate in units per hour:
- 6 workers × 12 = 72 units/hour.
Overtime hours needed:
- 108 ÷ 72 = 1.5 hours.
Cost:
- Overtime rate = $18 × 1.5 = $27/hour per worker.
- 6 workers × 1.5 hours × $27 = $243.
Cap check: $243 ≤ $1,000, so the plan fits with $757 to spare. In practice the manager should schedule a full 2-hour block (cost $324) to avoid a partial-shift edge case, still well under the cap.
3. A supplier offers to deliver the 108-unit shortfall as pre-packed units at $4.25 each instead of paying overtime. Using your overtime figure, which option is cheaper, and by how much?
Read the worked answer
Supplier cost: 108 × $4.25 = $459.
Overtime cost (minimum): $243.
Difference: $459 − $243 = $216.
Overtime is cheaper by $216. Note the comparison flips only if overtime must be paid in a full 2-hour block ($324) and the supplier price drops below about $3.00 per unit - a useful sensitivity check before committing.