Staffing and Costing the Seven-Day Road Safety Campaign
A district plans a seven-day road-safety campaign with three fixed checkpoints every day. Each checkpoint must be staffed by two officers for a four-hour shift. No officer may work more than one shift on the same day, and no officer may work more than five shifts across the seven days. The district has 21 trained officers, but 4 are on annual leave for the whole week and 2 are on a training course for the first three days only. Any shift worked on an officer's rest day is paid as overtime at €14 per hour. Two vans are needed for the whole campaign; each van covers 45 km per day and costs €0.32 per km. The campaign has a total budget of €1,500 to cover overtime and vehicle costs. Separately, a radar log for one morning records three vehicles - a white van, a red car and a motorcycle - at speeds of 46, 49 and 63 km/h in some order. The limit is 50 km/h. The vehicle over the limit was not the motorcycle; the motorcycle was faster than the car; the van was not the slowest.
1. Can the campaign be staffed with the officers available? Show the required shifts, the available officer-shifts, the effect of the training course, and the minimum number of officers that would be needed.
Read the worked answer
Required shifts
3 checkpoints × 2 officers = 6 officer-shifts per day. 6 × 7 days = 42 officer-shifts of four hours each.
Available officers
- Trained establishment: 21
- Annual leave, whole week: −4 → 17 available in total
- Training course, days 1–3 only: −2 → 15 available on days 1, 2 and 3; 17 on days 4–7.
Checking against the constraints
- Per-day need is 6, and even the worst day has 15 available, so the one-shift-per-day rule is easily satisfied.
- Total capacity under the five-shifts-in-seven-days cap: 17 × 5 = 85 officer-shifts, against 42 required. Load is about 42 ÷ 17 ≈ 2.5 shifts per officer.
Minimum number of officers
An officer can cover at most 5 shifts in the week, so 42 ÷ 5 = 8.4 → at least 9 officers are needed, provided they are all available on the days required. The campaign is comfortably feasible with the 17 available.
2. Twelve of the 42 shifts must be paid as overtime. Calculate the overtime cost and the vehicle cost, decide whether the €1,500 budget is sufficient, and state how many further overtime shifts could be paid within the budget.
Read the worked answer
Overtime
Each shift is 4 hours at €14 per hour = €56. 12 shifts × €56 = €672.
Vehicles
2 vans × 45 km per day × 7 days = 630 km. 630 km × €0.32 = €201.60.
Total and budget test
€672.00 + €201.60 = €873.60. €1,500 − €873.60 = €626.40 remaining. The budget is sufficient.
Further overtime shifts
€626.40 ÷ €56 = 11.18 → 11 more full shifts (11 × €56 = €616.00), leaving €10.40 unspent. A twelfth shift would cost €56 and exceed the headroom, so it would need separate authorisation.
Note for the answer: keep the two cost lines separate. Mixing the €56 per-shift rate with the €0.32 per-km rate is the common error - one is per shift, the other per kilometre.
3. Determine the speed of each vehicle, showing each deduction step, and state which vehicle must be reported.
Read the worked answer
Given: speeds 46, 49 and 63 km/h; limit 50 km/h, so only the 63 km/h vehicle is over the limit.
Step 1 - which vehicles could be the 63 km/h one? The over-limit vehicle is not the motorcycle, so it is the van or the car.
Step 2 - could it be the car? The motorcycle was faster than the car. If the car were 63 km/h, nothing in the set is faster than 63, so no speed could be assigned to the motorcycle. The car therefore cannot be the 63 km/h vehicle.
Step 3 - assign The van = 63 km/h. This also satisfies "the van was not the slowest".
Step 4 - the remaining two Remaining speeds are 46 and 49 for the car and the motorcycle. The motorcycle is faster than the car, so:
- Motorcycle = 49 km/h
- Car = 46 km/h
Step 5 - consistency check Van 63 (fastest, over the limit), motorcycle 49 (not slowest among the three but slower than the van), car 46 (slowest). Van not the slowest ✓; motorcycle faster than car ✓; over-limit vehicle not the motorcycle ✓.
Conclusion: the white van at 63 km/h is 13 km/h over the limit and is the only vehicle to be reported. The car and motorcycle were within the limit and require no further action.