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A hotel purchases 20 kg of beef at KSH 600 per kg. After trimming, only 16 kg is usable. Calculate the yield percentage and the number of portions if the standard portion size is 250 grams.

Business/Management

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Step-by-step solution

9 steps

Here's the solution to the food production problem:

Part b(i)· 3 steps

Calculate the yield percentage.

In food production, not all purchased quantity is usable due to trimming, bones, fat, or waste. A hotel purchases 20 kg of beef at KSH 600 per kg. After trimming, only 16 kg is usable.

  1. Identify the original purchased quantity and the actual usable quantity.

    Original Purchased Quantity = 20 kg20 \text{ kg}
    Actual Usable Quantity = 16 kg16 \text{ kg}

  2. Use the formula for yield percentage.

    Yield Percentage=Actual Usable QuantityOriginal Purchased Quantity×100%\text{Yield Percentage} = \frac{\text{Actual Usable Quantity}}{\text{Original Purchased Quantity}} \times 100\%

  3. Substitute the values and calculate.

    Yield Percentage=16 kg20 kg×100%\text{Yield Percentage} = \frac{16 \text{ kg}}{20 \text{ kg}} \times 100\% Yield Percentage=0.8×100%\text{Yield Percentage} = 0.8 \times 100\% Yield Percentage=80%\text{Yield Percentage} = 80\%

    The yield percentage is 80%\boxed{\text{80\%}}.

Part b(ii)· 6 steps

If the standard portion size is 250 grams, calculate

  • The number of portions available

  1. Convert the total usable quantity from kilograms to grams.

    1 kg=1000 grams1 \text{ kg} = 1000 \text{ grams}
    Total Usable Quantity = 16 kg×1000 g/kg=16000 g16 \text{ kg} \times 1000 \text{ g/kg} = 16000 \text{ g}

  2. Divide the total usable quantity by the standard portion size.

    Number of Portions=Total Usable QuantityStandard Portion Size\text{Number of Portions} = \frac{\text{Total Usable Quantity}}{\text{Standard Portion Size}} Number of Portions=16000 g250 g/portion\text{Number of Portions} = \frac{16000 \text{ g}}{250 \text{ g/portion}} Number of Portions=64 portions\text{Number of Portions} = 64 \text{ portions}

    The number of portions available is 64 portions\boxed{\text{64 portions}}.

    • The food cost per portion (using edible portion cost)

  3. Calculate the total cost of the purchased beef.

    Total Cost=Purchased Quantity×Cost per kg\text{Total Cost} = \text{Purchased Quantity} \times \text{Cost per kg} Total Cost=20 kg×KSH 600/kg\text{Total Cost} = 20 \text{ kg} \times \text{KSH } 600/\text{kg} Total Cost=KSH 12000\text{Total Cost} = \text{KSH } 12000

  4. Calculate the edible portion cost per kilogram (the actual cost per kg of usable beef).

    Edible Portion Cost per kg=Total CostActual Usable Quantity\text{Edible Portion Cost per kg} = \frac{\text{Total Cost}}{\text{Actual Usable Quantity}} Edible Portion Cost per kg=KSH 1200016 kg\text{Edible Portion Cost per kg} = \frac{\text{KSH } 12000}{16 \text{ kg}} Edible Portion Cost per kg=KSH 750/kg\text{Edible Portion Cost per kg} = \text{KSH } 750/\text{kg}

  5. Convert the standard portion size from grams to kilograms.

    250 g=0.250 kg250 \text{ g} = 0.250 \text{ kg}

  6. Calculate the food cost per portion.

    Food Cost per Portion=Edible Portion Cost per kg×Standard Portion Size (in kg)\text{Food Cost per Portion} = \text{Edible Portion Cost per kg} \times \text{Standard Portion Size (in kg)} Food Cost per Portion=KSH 750/kg×0.250 kg\text{Food Cost per Portion} = \text{KSH } 750/\text{kg} \times 0.250 \text{ kg} Food Cost per Portion=KSH 187.50\text{Food Cost per Portion} = \text{KSH } 187.50

    The food cost per portion is KSH 187.50\boxed{\text{KSH } 187.50}.

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