Scaling a Field Kitchen Recipe
A field kitchen is preparing a hot meal for 250 personnel at a training area. The catering sergeant's recipe card is written for 40 portions and lists 6.0 kg chicken, 2.5 kg rice, 1.2 kg sauce and 0.8 kg onions. Eight per cent of the 250 will be on stag and will eat 90 minutes later, but they still require a full portion. The kitchen allows 5% extra food for spillage and second helpings. Chicken is supplied in 5 kg frozen packs, rice in 10 kg sacks and sauce in 2.5 kg tubs. A delivery delay means only 38 kg of chicken is currently on the shelf. The head cook wants to know how much of each item to draw, whether the chicken draw will leave an open pack, whether the rice-to-chicken ratio stays the same as the card, and what to do about the chicken shortage.
1. Calculate the total number of portions to prepare, the scaling factor from the 40-portion card, and the quantity of each ingredient required.
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Stag personnel still eat, so the full 250 portions are required; the timing changes, not the quantity. Add 5% for spillage/second helpings: 250 × 1.05 = 262.5 → 263 portions. Round up, because 262 would be below the allowance. Scaling factor = 263 ÷ 40 = 6.575. Chicken = 6.0 × 6.575 = 39.45 kg. Rice = 2.5 × 6.575 = 16.44 kg (2 d.p.). Sauce = 1.2 × 6.575 = 7.89 kg. Onions = 0.8 × 6.575 = 5.26 kg. Rounding portions up rather than down protects the 5% allowance; the extra 0.5 portion is negligible but avoids systematically underfeeding.
2. Convert the ingredient quantities into store draws using the pack sizes. State the chicken position against the 38 kg on the shelf and whether an open pack remains.
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Chicken: 39.45 kg required; 5 kg packs → 39.45 ÷ 5 = 7.89 → 8 packs = 40 kg. Only 38 kg is on the shelf, so the kitchen is 1.45 kg short of the 39.45 kg requirement, or 2 kg short of the 40 kg draw. Eight packs would leave 40 − 39.45 = 0.55 kg in an open pack. Rice: 16.44 ÷ 10 = 1.64 → 2 sacks = 20 kg, leaving 3.56 kg. Sauce: 7.89 ÷ 2.5 = 3.16 → 4 tubs = 10 kg, leaving 2.11 kg. Onions have no stated pack size, so draw 5.26 kg; a practical issue would be about 5.3 kg.
3. The full 39.45 kg of chicken cannot be obtained. Using the 38 kg available, calculate how many personnel can be fed at the same recipe ratio and 5% allowance, and state the shortfall.
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Scale from the card using the available chicken: 38 kg ÷ 6.0 kg per 40 portions = 6.3333... card batches. Portions before waste allowance = 40 × 6.3333 = 253.33. The 5% allowance means only 253.33 ÷ 1.05 = 241.27 → 241 portions can be sustained. Against 250 personnel, that is 9 short. The other ingredients are not limiting: rice supports 20 ÷ 2.5 × 40 = 320 portions before waste, and sauce supports 10 ÷ 1.2 × 40 = 333, so chicken is the binding constraint. The cook should report a 9-portion chicken shortfall or substitute another protein; simply using 38 kg without recalculating would under-portion all 250 meals.