Optimizing Sugar Mixture Pricing for Maximum Profit

In the bustling world of grocery retail, calculating optimal pricing for products that are derived from various mixtures isessential. A grocer, for example, purchased 80 kg of sugar at Rs. 13.50 per kg and mixed it with 120 kg of sugar costing Rs. 16 per kg. To achieve a 16% profit, determining the correct selling price per kg is crucial. In this article, we will walk through the steps required to achieve this goal, leveraging cost price calculations and mixture pricing strategies.

Step 1: Understanding the Problem and Key Data

The problem involves a grocer who has mixed two types of sugar. The first type weighs 80 kg and costs Rs. 13.50 per kg, while the second type weighs 120 kg and costs Rs. 16 per kg. The aim is to mix these two types of sugar and sell them at a price that would yield a 16% profit.

Step 2: Calculating the Cost of Each Type of Sugar

The first step in solving this problem is to calculate the cost of each type of sugar.

For the first type of sugar:

Weight 80 kg Cost per kg Rs. 13.50

Cost of the first type of sugar 80 kg × 13.50 Rs/kg 1080 Rs

For the second type of sugar:

Weight 120 kg Cost per kg Rs. 16

Cost of the second type of sugar 120 kg × 16 Rs/kg 1920 Rs

Step 3: Total Cost and Total Weight of the Mixture

The next step is to calculate the total cost and total weight of the mixture.

Total Cost Cost of the first type of sugar Cost of the second type of sugar 1080 Rs 1920 Rs 3000 Rs Total Weight Weight of the first type of sugar Weight of the second type of sugar 80 kg 120 kg 200 kg

Step 4: Cost Price per kg of the Mixture

The cost price per kg of the sugar mixture is calculated by dividing the total cost of the mixture by the total weight of the mixture.

Cost Price per kg Total Cost / Total Weight 3000 Rs / 200 kg 15 Rs/kg

Step 5: Determining the Selling Price for 16% Profit

Finally, the grocer needs to determine the selling price per kg to achieve a 16% profit.

Selling Price per kg Cost Price per kg 16% of Cost Price per kg

Selling Price per kg 15 Rs/kg 0.16 × 15 Rs/kg 15 Rs/kg 2.4 Rs/kg 17.4 Rs/kg

Conclusion

The grocer should sell the mixture at Rs. 17.40 per kg to gain a 16% profit.

Optimizing the pricing of such mixtures requires a clear understanding of the cost structure and the desired profit margin. By accurately calculating the cost price and applying the appropriate profit margin, retailers can ensure they maximize their profits while remaining competitive in the market.

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