Fuel Resupply for a Field Convoy
A convoy must move 240 km from Base A to Outpost B. Each truck's tank holds 60 L and consumes 1.2 L per km when loaded. Trucks may carry one 20 L jerrycan each, but a full jerrycan adds weight that raises consumption to 1.35 L per km. Fuel is only available at A and B; no intermediate depots. The commander wants to send 3 identical trucks, each starting with a full tank and one full jerrycan. A safety rule requires every truck to arrive with at least 5 L in its tank. A staff officer claims the convoy can complete the trip without refueling en route.
1. Determine whether the officer's claim is correct, showing the fuel budget for one truck.
Read the worked answer
Total fuel per truck: 60 L (tank) + 20 L (jerrycan) = 80 L.
Consumption while carrying the jerrycan: 1.35 L/km.
Range on full load: 80 / 1.35 ≈ 59.3 km - far short of 240 km.
Even if the jerrycan were emptied immediately (so consumption drops to 1.2 L/km after the first stretch), the truck still has only 80 L total, giving a best-case range of 80 / 1.2 ≈ 66.7 km.
Conclusion: The officer is wrong. 240 km requires roughly 240 × 1.2 = 288 L per truck at best, versus 80 L available. The convoy cannot reach B without an intermediate fuel source or a different plan.
2. The commander proposes reducing to 2 trucks and using the third truck purely as a fuel carrier. Evaluate whether this changes the feasibility, and state what minimum total fuel the mission needs.
Read the worked answer
Minimum fuel for 2 delivering trucks (no jerrycan penalty if fuel is transferred early): each needs 240 × 1.2 = 288 L, so 2 × 288 = 576 L, plus 2 × 5 L reserve = 586 L.
Fuel the carrier can supply: one truck holds 60 L in its tank plus one 20 L jerrycan = 80 L total. Even if all of it is transferred, the convoy has 80 (carrier) + 80 + 80 = 240 L - still far below 586 L.
Conclusion: Removing one truck makes it worse, not better. The carrier's 80 L cannot offset the loss of a delivering vehicle. The mission is infeasible under these constraints; the commander must add intermediate fuel, reduce distance, or use higher-capacity vehicles.