The Overloaded Ferry Manifest
A small ferry has a maximum safe load of 4,800 kg. The operator has already loaded 12 crates, each weighing 210 kg, and 3 vehicles weighing 640 kg, 725 kg, and 590 kg. A supplier arrives with a final pallet of identical boxes. Each box weighs 48 kg, and the pallet itself weighs 60 kg. Regulations require that after loading, at least 8% of the maximum safe load must remain as a safety margin. The supplier insists the whole pallet must go on or none of it.
1. Determine whether the full pallet can be loaded. Show the arithmetic for the current load, the safety-margin limit, and the maximum number of boxes that could be added.
Read the worked answer
Current load: crates = 12 × 210 = 2,520 kg. Vehicles = 640 + 725 + 590 = 1,955 kg. Total = 2,520 + 1,955 = 4,475 kg.
Safety margin = 8% of 4,800 = 384 kg. So usable capacity = 4,800 − 384 = 4,416 kg.
The current load (4,475 kg) already exceeds 4,416 kg, so the ferry is over its margin before any boxes are added. In fact it is above 4,416 by 59 kg.
Maximum boxes: allowable box+pallett weight = 4,416 − 4,475 = −59 kg. A negative allowance means zero boxes can be added; the pallet cannot be loaded. The operator must remove weight first.
2. The supplier offers to leave the pallet behind and load only loose boxes. How many loose boxes (48 kg each, no pallet) can be added while respecting the 8% margin?
Read the worked answer
Allowance = 4,416 − 4,475 = −59 kg. Since even zero boxes leaves the ferry 59 kg over the margin, no loose boxes can be added either. The answer is 0 boxes.
This tests whether the solver notices that the constraint is already violated, rather than mechanically dividing 4,416 by 48. Dividing 4,416 ÷ 48 ≈ 92 would be wrong because it ignores the 4,475 kg already aboard. The correct conclusion: the ferry must shed at least 59 kg before any additional cargo is permitted.