Question

Casein, a dairy product used in making cheese, contains 25% moisture when wet. A dairy sells this product for $40/100 kg. If requested, they will dry the casein to 12% moisture. The drying costs are $5/100 kg of water removed. Assume that that the dairy has 1000 kg of the original product (wet casein) that will be dried to 12% moisture and then sold. How much dried casein is produced (in kg)?
The answer is 852 (with margin 1). Why is it?

Answer 1

Based on the percent moisture content of the dried product, the mass of dried casein produced os 852.3 kg.

What is the mass of casein in wet casein?

The mass of casein in 1000 Kg of wet casein is 75% 1000 kg = 750 Kg

Mass of water 250 kg

The mass of casein is constant while the moisture content can be changed.

At 12% moisture content;

750 kg = 88%%

100 % = 100 ×750/88 = 852.27 kg

Therefore, the mass of dried casein produced os 852.3 kg.

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