Ration Pack Draw for a Five-Day Exercise
Your training wing is planning a five-day field exercise for 186 recruits and 22 permanent staff. Ration packs are issued at one per person per day, and each pack weighs 1.8 kg. Packs arrive in boxes of 12, and boxes are stacked 40 to a pallet. The stores hold two full pallets plus nine loose boxes. The quartermaster also expects 6% additional personnel to attach at short notice, but no extra pallets can be delivered before the exercise starts. Transport is limited: one 4-tonne truck can carry 36 boxes per trip, and only three trips are available before the first meal. You must confirm whether the exercise can be supported from current stock, identify any shortfall, and advise the chain of command before orders are published.
1. Using the confirmed strength of 208 personnel, calculate the number of ration packs and full boxes required, and compare this with the stock held. State the surplus or shortfall in boxes and packs.
Read the worked answer
Confirmed strength = 186 + 22 = 208 personnel. Over 5 days: 208 × 5 = 1,040 packs. Boxes are whole units: 1,040 ÷ 12 = 86.67, so 87 boxes are needed. Using 86 boxes would give only 86 × 12 = 1,032 packs, leaving 8 people short on the final day. Stock = (2 × 40) + 9 = 89 boxes. Surplus = 89 − 87 = 2 boxes = 24 packs. The exercise can be supported from current stock with 24 packs spare, before any uplift is applied.
2. The 6% uplift is confirmed. Recalculate the personnel strength, packs and boxes, and state the shortfall against the 89 boxes held. Explain any rounding decision.
Read the worked answer
6% of 208 = 12.48. Personnel must be a whole number, and a partial person cannot be fed, so round up: 208 × 1.06 = 220.48 → 221 personnel. Packs = 221 × 5 = 1,105. Boxes = 1,105 ÷ 12 = 92.08 → 93 boxes. Stock is 89 boxes, so the shortfall is 4 boxes. Those 4 boxes contain 48 packs, against a requirement of 1,105 − (89 × 12 = 1,068) = 37 packs, leaving 11 packs spare. Rounding up boxes rather than packs is correct because packs are issued in sealed boxes; ordering 92 boxes would leave 1,104 packs, one pack short.
3. A clerk argues the 6% should be applied only to the 186 recruits, not to the 208 total. Test that assumption and state the practical difference in boxes.
Read the worked answer
Recruit-only uplift: 186 × 1.06 = 197.16 → 198 recruits. Add 22 staff = 220 personnel. Packs = 220 × 5 = 1,100. Boxes = 1,100 ÷ 12 = 91.67 → 92 boxes. The total-strength method gave 93 boxes, so the clerk's method understates the draw by 1 box (12 packs). The difference arises because 6% of 208 (12.48) rounds to 13 extra people, whereas 6% of 186 (11.16) rounds to 12 extra recruits; the staff are not uplifted in the clerk's method. Given the wording 'additional personnel', the safer planning assumption is 221 personnel, because a one-box error at issue would leave the final meal short.