Optimizing Profit in Mixture Blending: A Case Study with Milk and Water

When blending milk and water to maximize profit, it is essential to understand the underlying principles of cost price and selling price. This article explores how to achieve a desired profit margin by mixing milk and water in the correct proportions.

Understanding the Basics: Profit and Cost Price

A business needs to calculate the cost price of its ingredients (milk, in this case) and the selling price to achieve a certain profit margin. By understanding these fundamentals, businesses can optimize their mixture blending to ensure maximum profitability.

Methodology: Achieving a 16% Profit Margin

To determine the optimal ratio of water and milk needed to achieve a 16% profit margin, we follow a systematic approach.

Step 1: Define Variables

Let the cost price of milk per liter be C.

The selling price for a 16% profit would be SP C 0.16C 1.16C.

Step 2: Assume Quantities

We assume the quantity of milk is 1 liter.

Let the quantity of water be x liters.

Step 3: Calculate the Total Cost Price

The total cost price of the mixture, which includes milk and water, is simply the cost of the milk, as water is assumed to have a negligible cost:

Total Cost Price (CP) C

Step 4: Calculate the Selling Price

The total volume of the mixture is 1 x liters. The selling price of the mixture based on the desired profit is:

SP 1.16C (1 x)

Selling Price per liter of the mixture can be calculated as:

Selling Price per liter SP / (1 x) 1.16C / (1 x)

Since the selling price per liter must equal the cost price per liter for the mixture to achieve a 16% profit:

1.16C / (1 x) C / 1

Step 5: Solve for x

Cross-multiplying gives:

1.16C C * (1 x)

Dividing both sides by C (assuming C ≠ 0):

1.16 1 x

Rearranging gives:

x 1.16 - 1 0.16

Step 6: Determine the Ratio

The ratio of water to milk is:

Ratio of water to milk x / 1 0.16 / 1 0.16:1

Multiplying both sides by 100 to express this in whole numbers:

Ratio 0.16 * 100 : 1 * 100 16 : 100 4 : 25

Conclusion: Achieving Optimal Profit with Milk and Water

The optimal ratio in which water must be mixed with milk to achieve a 16% profit margin on the selling mixture at cost price is 4:25. This approach can be adjusted for different profit margins, as shown in the example for a 20% profit. By following these calculations, businesses can optimize their mixture blending processes and achieve the desired profit margins.