In the ice cream manufacturing process, you must carefully weigh and measure the ingredients before starting to mix. You must carefully identify the amount of each ingredient you use to formulate ice cream mix due to:

*A finished product of the right quality and consistency from batch to batch is very necessary*. It is only possible to achieve this by using the right proportions of the ingredients.*The cost implications.*Some ingredients such as cream are expensive; therefore, the manufacturer may compromise on the quality of the product.

Here's a video of mix formation.

Video by Jeff Brackenbury

To ensure that you end up with the right formulation of the mix, you can adopt any of these methods:

- Pearson square method
- Algebraic equations method
- Calculating the percentage MSNF
- Serum point method
- Formula (tables) method
- Computer generated formulations

We will use a problem to demonstrate how to formulate an ice cream formula using one of the listed methods.

Algebraic equations method to formulate ice cream mix

Formulate a 10,000 kg ice cream mix with 12% butterfat, 10% MSNF, 14% cane sugar, 0.2% gelatin, 0.2% glycerol monostearate, and 0.3% flavor/color combination.

## Ingredients to formulate ice cream mix

- Fresh cream: 38.5% BF and 5.5% MSNF
- Whole milk: 3.5% BF and 8.5% MSNF
- Skim milk powder: 0% BF and 96% MSNF
- Gelatin: 100% TS
- Gums: 100% TS
- Flavor and color: 100% TS

### Questions

- Calculate the amount of each ingredient to be used to formulate ice cream mix above.
- The mix was used to make ice cream with 80% overrun: Calculate the final weight of the ice cream.

### Answers

Now, assuming x-cream, y-whole milk powder, and z-skim milk powder,

**The total mix equation (i)** becomes:

x+y+z+14+0.2+0.2+0.3=100 ===> x+y+z=85.3

**Butterfat equation (ii)** becomes:

(38.5/100)x+(3.5/100)y=12 ===> 0.385x+0.035y=12

**MSNF equation (iii)** becomes:

0.055x + 0.085y + 0.96z = 10

**Eliminate z by multiplying equation (i)** by 0.96

0.96x + 0.96y + 0.96z = 81.888……….(iv)

**Equate equation (iv) with equation (iii)**

*{0.96x + 0.96y + 0.96z = 81.888} - {0.055x + 0.085y + 0.96z = 10} = {0.905x + 0.875y = 71.888}*

Make x the subject of the formula

0.905x = 71.888 - 0.875y ===> x = 79.4343 - 0.9669y

**Now substitute x in equation (ii)**

Equation (ii) is 0.385x + 0.035y = 12

Substituting x gives:

0.385(79.4343 - 0.9669y) + 0.035y = 12 ===> 30.547 - 0.3723y + 0.035y = 12

18.547 = 0.3373y ===> y = 54.987kg

**Substitute the value of y in equation (ii)**

Equation (ii) is 0.385x+0.035y=12

Substituting y gives

0.385x+0.035(54.987) = 12

0.385x = 10.075 ===> x = 26.17kg

**Substitute the values of x and y in equation (i)** to get the value of z

Equation (i) is x+y+z=85.3

26.17+54.987+z=85.3 ===> z=85.3-81157 ===> z=4.143kg

To get the amounts of each ingredient used to make the 10,000 mix

X=26.17*100=2617kg of cream

Y=54.987*100=5498.7kg of whole milk

Z=4.143*100=414.3kgof skim milk powder

- Sugar needed = 1400kg
- Flavor and color = 30kg
- GMS = 20kg
- Gelatin = 20kg

Total amount of ice cream mix = 1400+30+20+20+414.3+5498.7+2617 = 10,000kg

With 80% overrun, the final quantity of the ice cream becomes 10,000*1.8 = 18,000kg.

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