Optimizing Price to Minimize Loss and Maximize Profit: A Case Study on Mango Sales
Effective pricing is a critical strategy in any business, especially in retail. In this article, we delve into a real-world scenario involving the sale of mangoes. We will explore the mathematics behind calculating the selling price to minimize loss and the price to maximize profit. This case study is invaluable for any entrepreneur looking to streamline their business operations and improve profitability.
Scenario Overview
A fruit seller sells mangoes at the rate of Rs. 40 per kg and thereby incurs a loss of 10%. We will calculate the cost of 1 kg of mangoes and then determine the selling price per kg that would ensure a 15% profit.
Calculating the Cost Price of Mangoes
The first step is to determine the cost price of 1 kg of mangoes. Let's assume the cost price is Rs. 10. With a loss of 10%, the selling price is 90% of the cost price.
Mathematically, we can express this as:
Selling Price (SP) Cost Price (CP) – Loss
Given that the selling price is Rs. 40 and the loss is 10%, we can write:
40 CP – (CP * 0.10)
40 0.90 * CP
CP 40 / 0.90
CP Rs. 44.44 per kg
However, the provided data suggests a direct calculation method. Let's validate the solution using this method:
Sales price per kg Rs. 40
Loss 10%
Cost price per kg 40 / (1 – 0.10) 40 / 0.90 Rs. 44.44 per kg
Determining the Selling Price for a 15% Profit
To maximize profit, the seller needs to sell the mangoes at a price that gives a 15% profit. Let's calculate this selling price.
For a 15% profit, the new selling price (SP) can be calculated as:
SP CP * (1 Profit Percentage)
CP Rs. 44.44 (from above calculation)
Profit 15%
SP 44.44 * (1 0.15) 44.44 * 1.15 Rs. 51.12 per kg
Hence, the fruit seller should sell the mangoes at Rs. 51.12 per kg to achieve a 15% profit.
Alternative Methods for Calculating the Selling Price
There are several methods to calculate the selling price for a desired profit. Here are a few approaches:
Method 1
Given the sales price per kg at a loss of 20% is Rs. 9:
Cost price per kg 9 / (1 – 0.20) 9 / 0.80 Rs. 11.25 per kg
To achieve a 15% profit, the new selling price (SP) is:
SP 11.25 * (1 0.15) 11.25 * 1.15 Rs. 11.8125 per kg
Method 2
Another method involves considering a 20% loss:
Sales price per kg at 20% loss Rs. 9
Cost price per kg 9 / (1 – 0.20) 9 / 0.80 Rs. 11.25 per kg
To achieve a 5% profit, the new selling price (SP) is:
SP 11.25 * (1 0.05) 11.25 * 1.05 Rs. 11.8125 per kg
Method 3
Consider a 20% loss and a 15% profit:
Cost price per kg 9 / (1 – 0.20) 9 / 0.80 Rs. 11.25 per kg
To achieve a 5% profit, the new selling price (SP) is:
SP 11.25 * (1 0.15) 11.25 * 1.15 Rs. 11.8125 per kg
Conclusion
By calculating the cost price and applying various profit percentages, we can determine the optimal selling price for maximum profit. This approach is crucial for any business seeking to improve its profitability and competitive edge in the market.
The key takeaway is that careful analysis of the current selling price, loss percentage, and desired profit percentage allows for precise price setting. This not only helps in minimizing loss but also in maximizing profit. Regularly revising and adjusting prices can help businesses stay competitive and adapt to market dynamics.