Dairy Blending: Toned Milk, Fat Standards and Opportunity Cost
A dairy cooperative in Rohtak buys raw milk from farmers, separates it into cream and skimmed milk, and sells toned milk. It has 800 litres of full-cream milk with 6.0% fat and 1,200 litres of skimmed milk with 0.5% fat. The cooperative wants to blend these into toned milk with exactly 3.0% fat. It can also sell any surplus full-cream or skimmed milk in the wholesale market at ₹42 per litre and ₹24 per litre respectively. Toned milk sells for ₹36 per litre. Blending and packaging cost ₹4 per litre of the final product. There is no loss in volume during blending.
1. Find the ratio of full-cream to skimmed milk needed to make 3.0% fat toned milk and the maximum litres of toned milk that can be made from the available stock.
Read the worked answer
Let the toned milk contain x litres of full-cream milk and y litres of skimmed milk. Fat balance:
6x + 0.5y = 3(x + y) 6x + 0.5y = 3x + 3y 3x = 2.5y x/y = 2.5/3 = 5/6
So the required ratio is full-cream : skimmed = 5 : 6.
Maximum output:
- If all 800 L of full-cream milk is used, required skimmed milk = 800 × 6/5 = 960 L. Total = 800 + 960 = 1,760 L.
- This uses only 960 L of the 1,200 L skimmed milk, leaving 240 L of skimmed milk.
- If all 1,200 L of skimmed milk were used, required full-cream milk = 1,200 × 5/6 = 1,000 L, which is more than the 800 L available. So full-cream milk is the limiting input.
Maximum toned milk = 1,760 litres, leaving 240 litres of skimmed milk.
2. Calculate the profit or loss per litre of toned milk versus selling the same components wholesale, and decide whether blending is worthwhile at ₹36 per litre.
Read the worked answer
For 1,760 L of toned milk, the cooperative uses 800 L full-cream and 960 L skimmed milk.
Opportunity cost of components:
- Full-cream: 800 × ₹42 = ₹33,600
- Skimmed: 960 × ₹24 = ₹23,040
- Total = ₹56,640
Processing and packaging: 1,760 × ₹4 = ₹7,040
Total cost of the toned milk = ₹56,640 + ₹7,040 = ₹63,680.
Revenue from toned milk = 1,760 × ₹36 = ₹63,360.
Loss = ₹63,680 − ₹63,360 = ₹320, or ₹320 ÷ 1,760 ≈ ₹0.18 per litre.
Including the 240 L surplus skimmed milk sold at ₹24 gives ₹5,760, but the comparison is unchanged: selling all milk wholesale gives 800 × 42 + 1,200 × 24 = ₹62,400, while toned milk plus surplus gives ₹63,360 + ₹5,760 − ₹7,040 = ₹62,080. The loss is still ₹320.
At ₹36, blending is not worthwhile. The minimum price is ₹63,680 ÷ 1,760 ≈ ₹36.19 per litre.
3. A customer claims the toned milk is 'adulterated' because it contains skimmed milk. Evaluate this claim using the fat standard and the nature of toned milk.
Read the worked answer
The claim confuses composition with contamination. Toned milk is a defined product made by blending full-cream or raw milk with skimmed milk to reach a specified fat level. Using skimmed milk to reduce fat from 6.0% to 3.0% is a standard formulation step, not adulteration, provided the final product meets the declared fat standard and is labelled correctly.
Adulteration would involve adding substances not permitted in milk-such as unclean water, starch, detergent or preservatives-or selling a product below its declared standard. The customer has identified an ingredient, not a prohibited additive.
The cooperative should be able to show its fat testing records and FSSAI-compliant labelling. If the toned milk actually tests below 3.0% fat, or if the label misrepresents the composition, then a regulatory issue arises. On the facts given, the mere presence of skimmed milk does not make the product adulterated.