Application of the Derivative Concept to Determine the Maximum Profit Point of Nasi Lengko Traders in Cirebon

Abstract

This study employs the concept of differentials, or mathematical derivatives, to determine the maximum profit points for Cirebon-style Nasi Lengko UMKM, namely Trader A and Trader B, both located in Sunyaragi Village. The study employs a quantitative descriptive approach, using interview data on capital, selling price, revenue, and production quantity. The data are then formulated as functions of total cost, revenue, and profit, using the first derivative to identify the critical points and the feasible domain. The results show that Trader A, with a capital of Rp 101,000 and a capacity of 20 portions, obtains a maximum profit of Rp 99,000 when all production is allocated to egg Nasi Lengko priced at Rp 10,000 per portion, due to a constant negative derivative. Meanwhile, Trader B, with a capital of Rp 200,000 and a capacity of 40 portions, achieves a maximum profit of Rp 200,000 by producing Nasi Lengko at a price of Rp 10,000 per portion, with a constant positive derivative. This study demonstrates that the concept of derivatives can help optimise production decisions in traditional food UMKM, despite limitations such as a small sample size and limited variable-cost data. Further studies are recommended to use a wider sample and more comprehensive data.