Analisis Konvergensi Newton–Raphson dalam Estimasi Titik Impas Penjualan Telur Ayam Kampung UMKM Surabaya

Free-range chicken eggs are an important commodity traded by Micro, Small, and Medium Enterprises, with prices that fluctuate across local markets and affect production planning. This study applies a nonlinear cost–revenue model and the Newton–Raphson method to determine the break-even point (BEP) using monthly price data from six traditional markets in Surabaya from January to October 2025. The analysis shows that most markets converge to a stable price of Rp48,000/kg, while markets with higher volatility require multiple iterations. The average selling price is Rp46,201.90/kg, forming the revenue function TR = 46,201.90Q and the cost function TC(Q) = 1,500,000 + 35,000Q. The BEP is achieved at Q* = 117.10 kg with total revenue equal to total cost of Rp5,410,040. These results confirm that the Newton–Raphson method provides stable and reliable BEP estimates for small-scale egg businesses