Estimating the Coastal Path Survey
A council is estimating the cost of surveying a 27 km coastal path. A pilot survey of 3.6 km took two surveyors 4.5 days. The full survey must be finished in 18 working days. Surveyors cost €240 per surveyor per day. The council's rough budget is €12,000. A manager estimates by rounding the pilot rate to 'about 1.25 days per km per surveyor' and multiplying by the full length and by two surveyors. An engineer warns that rounding this early distorts the total and that the real constraint is the 18-day deadline, not the money.
1. Using the exact pilot rate, calculate how many surveyor-days the full 27 km survey needs, and how many surveyors are required to finish within 18 working days.
Read the worked answer
Pilot: 2 surveyors × 4.5 days = 9 surveyor-days for 3.6 km. Rate = 9 ÷ 3.6 = 2.5 surveyor-days per km.
Full survey = 2.5 × 27 = 67.5 surveyor-days.
Surveyors needed for 18 days = 67.5 ÷ 18 = 3.75 → round up to 4 surveyors (3 would take 22.5 days, missing the deadline).
2. Compare the manager's rounded estimate (1.25 days per km per surveyor × 27 km × 2 surveyors) with the exact surveyor-day figure, and explain the source of the error.
Read the worked answer
Manager: 1.25 × 27 × 2 = 67.5 surveyor-days. Exact: 67.5 surveyor-days.
They match here - but only by coincidence of the numbers chosen. The manager's method is fragile: the true per-km-per-surveyor rate is 4.5 ÷ 3.6 = 1.25, so this particular rounding happened to be exact. The warning about early rounding is valid in principle (it can distort totals), but on these figures the estimate is correct. The judgement call is to verify rather than assume the rounded figure is wrong.
3. Calculate the labour cost with 4 surveyors over 18 days and assess it against the €12,000 budget. Is money or time the binding constraint?
Read the worked answer
Cost = 4 surveyors × 18 days × €240 = €17,280.
Budget is €12,000, so the plan is €5,280 over budget (44% over).
Money is the binding constraint, not time: 4 surveyors meet the deadline but blow the budget. With €12,000 you could afford 12,000 ÷ 240 = 50 surveyor-days, which at 2.5 per km covers only 20 km - short of 27 km. The engineer's claim that time is the constraint is wrong; cost is. The council must either extend the deadline or raise the budget.