# Problems

Below are some example problems to look at, if you are interested in the mathematics of mix calculations.

- Example 1. Basic mix using butter, skim powder, and water (only one source of each component). (Algebraic Method)
- Example 2. Mix using cream, skim, and skim powder (three sources of milk SNF, three sources of water). (Algebraic and Serum Point Methods)
- Example 3. Mix using cream, milk, and skim powder (three sources of milk SNF, three sources of water, and two source of fat). (Algebraic and Serum Point Methods)
- Example 4. Mix using cream, milk, and sweetened, condensed skim (three sources of milk SNF, three sources of water, two sources of fat, and two sources of sugar). (Serum Point Method)
- Example 5. Mix using cream, milk, and sweetened, condensed milk (three sources of milk SNF, three sources of water, three sources of fat, and two sources of sugar). (Serum Point Method)
- Example 6. Mix using a given amount of cream and skim, with the balance coming from butter, milk, and skim powder. (Serum Point Method)
- Example 7. Mix using cream, milk, condensed skim, and liquid sweeteners (water needs to be accounted for). (Serum Point Method)

After completing a problem, you should do a proof of your calculation, by ensuring that the mass sums to the desired value, and that the mass fraction of all components also sum to the desired value - see all the examples below. There is only one unique solution, so you know by calculation if you have it right or not!

Note: these are all solved on the basis of 100 kg. If you are making more or less than that, you can still solve on the basis of 100 kg and then scale up or down your answer accordingly (by dividing your answers per 100 kg by 100 and multipying by the actual wt., e.g. 45 kg cream/100 kg mix, if you are making 4000 kg, it would be 45/100*4000=180 kg cream) , or you can use the desired weight directly in the calculations, but be careful with the serum point method equations - see Example 3 below. If you have scaled up or down from 100 kg, you should do the proof total on the desired weight, and ensure it meets the desired percentage - see Example 3 or 6.

I am sometimes asked how to incorporate whole milk powder into mix calculations. This is common in some parts of the world. I will attach a pdf file below that shows such a calculation.