Four Days, Five Agents, Twelve Shifts
Surveillance is authorized for four consecutive days, Thursday through Sunday. Each day requires three 8-hour shifts: front post days (0600-1400), front post evenings (1400-2200), and rear post (1000-1800). Five agents are assigned: Kowalski, Adeyemi, Ruiz, Traynor, and Reese. Policy: no agent accumulates more than 20 hours without written overtime approval; no agent may exceed 28 hours; each shift is staffed by exactly one agent; an agent works no more than one shift per day. Reese attends required training Saturday and Sunday and cannot work those days. Overtime is paid at 1.5 times the $42 hourly base. The supervisory special agent must approve the minimum overtime needed before the operation begins.
1. How many shifts must be filled, and can the five agents cover them without exceeding 20 hours each?
Read the worked answer
Shifts: 3 per day x 4 days = 12 shifts, or 96 agent-hours.
The trap is to compare 96 hours to the team ceiling of 5 x 20 = 100 hours and conclude "no overtime needed." That comparison ignores that shifts are indivisible 8-hour blocks.
Because each shift is 8 hours:
- 2 shifts = 16 hours, within the 20-hour threshold.
- 3 shifts = 24 hours, which exceeds 20 and requires approval (it does not exceed the 28-hour hard cap).
So the maximum any agent can work without overtime approval is 2 shifts, and the team's no-overtime maximum is 5 x 2 = 10 shifts. Ten is less than the 12 required, so at least 2 extra shifts must be assigned to agents already holding 2 shifts.
Minimum number of agents in overtime: 2, each at 24 hours.
2. Compute the minimum overtime hours and cost, then demonstrate a schedule that achieves it while honoring Reese's unavailability.
Read the worked answer
Overtime: 2 agents x (24 - 20) = 8 overtime hours. Cost = 8 x ($42 x 1.5) = 8 x $63 = $504. No agent reaches the 28-hour cap (24 is the maximum).
Feasible schedule (one shift per agent per day; Reese only Thursday and Friday):
| Day | 0600-1400 | 1000-1800 | 1400-2200 |
|---|---|---|---|
| Thu | Reese | Kowalski | Adeyemi |
| Fri | Reese | Ruiz | Traynor |
| Sat | Kowalski | Adeyemi | Ruiz |
| Sun | Kowalski | Traynor | Adeyemi |
Totals: Reese 2, Ruiz 2, Traynor 2, Kowalski 3 (24 h), Adeyemi 3 (24 h) = 12 shifts. Exactly 2 agents cross 20 hours, matching the minimum computed above.
Note why the weekend does not break it: Thursday and Friday offer 6 shifts, Reese takes 2, and the other four take 1 apiece. The weekend's 6 remaining shifts fall on those four agents, each of whom has room for 1 more shift without overtime (4 shifts) - so exactly 2 must take a third.
3. The approving official asks whether a sixth agent would eliminate the overtime, and whether cutting the rear post on Sunday would. Evaluate both.
Read the worked answer
Sixth agent: yes, cleanly. With 6 agents the no-overtime ceiling becomes 6 x 2 = 12 shifts, exactly the requirement. Every agent works 2 shifts and nobody exceeds 16 hours. Feasibility holds with Reese's restriction: Reese takes 2 of the 6 Thursday/Friday shifts, the other five agents absorb the remaining 10 shifts at 2 apiece. Zero overtime.
Cutting the Sunday rear post: yes, but only by changing the requirement. That removes 1 shift (11 total), so the no-overtime ceiling of 10 is still short by one - 1 agent would still work a third shift. Cutting a shift on both Saturday and Sunday drops the total to 10, matching the ceiling exactly, at the cost of 16 hours of rear coverage during the weekend, when the residence is most likely occupied.
Recommendation: The $504 is the cheapest option that preserves the authorized coverage. Adding a sixth agent avoids the cost but adds a person to the operation and to any disclosure obligation. Reducing coverage saves money by removing surveillance, which is a substantive decision for the case agent, not a budget decision for the approver - the two should not be presented as equivalent choices.