Arithmetic of Ration and Patrol Fuel
A border outpost holds 240 kg of rice for 40 personnel. Daily consumption is 0.6 kg per person. A supply convoy is scheduled to arrive in 12 days but has been delayed twice already, and the sector office warns it may be delayed by up to 5 more days. Separately, the outpost has 90 litres of patrol fuel. Each patrol vehicle consumes 3 litres per 10 km, and a standard patrol route is 40 km round trip. The commander must decide whether to reduce the rice ration, reduce patrol frequency, or both, and must keep at least one patrol per day for border coverage.
1. Calculate how many days the rice will last at the current ration and at a reduced ration of 0.45 kg per person per day. Show your working.
Read the worked answer
Daily consumption at 0.6 kg per person for 40 personnel is 0.6 × 40 = 24 kg per day. At 240 kg, the rice lasts 240 ÷ 24 = 10 days. That is short of the 12-day scheduled arrival and far short of a 17-day worst case. At a reduced ration of 0.45 kg per person, daily consumption is 0.45 × 40 = 18 kg per day, and 240 ÷ 18 = 13.3 days. Even the reduced ration does not cover a 17-day delay, so rationing alone is insufficient; the commander must also request an emergency resupply or a partial air drop, and should begin rationing immediately rather than waiting.
2. Calculate how many standard patrols the fuel allows, and recommend a patrol plan that preserves daily coverage for as long as possible.
Read the worked answer
One standard patrol uses 40 km ÷ 10 km per 3 litres = 4 × 3 = 12 litres. With 90 litres, the outpost can run 90 ÷ 12 = 7.5, so 7 full patrols. If one patrol per day is required, fuel covers 7 days, not the 12-day minimum supply window. Options: shorten the route to 20 km round trip, which uses 6 litres and gives 15 patrols, or alternate a full patrol with a short patrol. A practical plan is to run a 20 km patrol on alternate days and a 40 km patrol on the others, averaging 9 litres per day, which stretches 90 litres to 10 days. The commander should also report the fuel shortfall to sector so resupply is prioritized alongside food.
3. Combine the two constraints and state the single most urgent action.
Read the worked answer
Food runs out at day 10 on full ration or day 13.3 on reduced ration; fuel runs out at day 7 on full patrols or about day 10 on mixed patrols. The binding constraint is fuel, which fails first. The most urgent action is to report both shortfalls to sector headquarters immediately with the arithmetic, request emergency fuel and food, and start reduced rice rationing on day 1 so the food buffer is preserved. Reducing patrols below one per day is not acceptable for border coverage, so the route must be shortened rather than the frequency cut.