Problem 4

Desired: 100 kgs. mix testing 14% fat, 10% MSNF, 15% sucrose, 0.5% stabilizer/emulsifier.

On hand: Cream 32% fat, milk 3.5% fat, sweetened condensed skim milk 28% serum solids and 40% sugar, sucrose and stabilizer.

Solution via the Serum Point Method :

1. Find amount of condensed skim milk required by the following formula:

(SNF needed - (serum of mix x .09))/( % SNF in cond. - (serum of cond. x .09)) x 100 = sweet cond. skim milk

Note: Serum of condensed is calculated the same as serum of mix, i.e., 100 - (Fat + Sugar + Stab.)

Substituting we have:

(10 - ( 70.5 x .09 ))/(28 - ( 60 x .09 )) x 100 = 16.17 kg cond. skim milk

2. Find amount of sucrose needed:

16.17 x .40 = 6.47 kg of sucrose in the condensed milk.
15 - 6.47 = 8.53 kg of sucrose still needed.

Note: If you added too much sugar by using sweetened condensed skim to supply the desired serum solids, then scale back the sweetened condensed skim to supply all the sugar you need and make up the deficiency in serum solids with skim powder.

3. Amount of stabilizer required is 0.5 kg.

4. Find weight of milk and cream needed.

Material so far supplied is, 16.17 kg condensed milk, 8.53 kg sugar and .5 kg stabilizer, a total of 25.2 kg.
100 - 25.2 = 74.8 kg milk and cream required.

5. Find amount of cream by the following formula:

((kg fat needed - (kg cream and milk needed x (% fat in milk/100)))/(% fat in cream - % fat in milk)) x 100

Substituting we have:
(14 - ( 74.8 x .035 ))/(32 - 3.5) x 100 = 39.93

6. Find milk required:

74.8 - 39.93 = 34.87 kgs. milk.

PROOF:

Ingredient Total wt. (kg) Wt. of Fat (kg) Wt. of SNF (kg) Wt. of Sugar (kg) Wt. of Total Solids (kg)
Cream 39.93 12.78 2.44 -- 15.22
Milk 34.87 1.22 3.03 -- 4.25
Swt. Cond. Milk 16.17 -- 4.53 6.47 11.00
Sucrose 8.53 -- -- 8.53 8.53
Stabilizer 0.50 -- -- -- 0.50
Totals 100.00 14.00 10.00 15.00 39.50

Note: 14% fat + 10% snf + 15% sucrose + 0.5% stab = 39.5% TS