# Calculations

Suppose a processor wishes to make process cheese food of legal composition(46% moisture, 22% fat). To allow for error he decides to set his target composition at 43% moisture and 24% fat. The ingredients on hand are Colby cheese (42% moisture, 29% fat), Cheddar cheese (39% moisture, 30 % fat), butter (16% moisture, 80% fat), whey powder (70% lactose, <1% fat, 4% moisture) and additives. Calculate the formula required for a 10 kg batch given that the weight of condensate added is 10% of the batch and the amount of cheese added is 70% of the batch of which 75% is Cheddar (75% of 70). See the composition control sheet and follow these steps:

1. Enter the final cheese composition and batch weight in the `Total' row.
2. Enter the composition of the ingredients.
3. Enter the total amounts (as percentage values) of Cheddar (75% of 70) and Colby (25% of 70) in the 'Total' column.
4. Calculate the amounts (in percentages) of fat, moisture and NSF contributed by the cheese. For example, the fat contributed by Cheddar is 30% of 52.6.
5. Calculate the percentage of fat required to bring the total fat to 24%, i.e., 24 - (5.1 + 15.8) = 3.1 and enter this value in the `Fat' column opposite 'Butter'.
6. Calculate the total amount (% of batch) of butter required (3.1 x 100/80 = 3.9) The amount of moisture (16% of 3.9) and solids-non-fat (4% of 3.9) contributed by butter can now be calculated.
7. Enter the required percentage amounts of the various additives. Calculate the amount of additional NSF required to bring the total to 33%. Enter this amount in the NSF column for whey protein concentrate. Note, any combination of whey powder, skim milk powder or whey protein concentrate can be used to adjust NSF providing the total amount of lactose is less than 15% of the cheese moisture.
8. Enter the amount of water contributed by condensate and calculate the amount of additional water required.
9. Determine the totals of each column and row to check your calculations.
10. Calculate the amounts of ingredients required per batch.

Note: The example given above is relatively simple and requires only simple arithmetic. However, consider the case where a manufacturer has quantities of high moisture cheese which he wishes to utilize in processing. He may then need to calculate the maximum amount of this cheese which can be used to replace cheddar without exceeding the legal moisture content. In this and similar cases the various unknowns must be defined in terms of required amounts of fat, NSF and moisture and the resulting equations solved simultaneously.