A Calculus Based Rice Production Scenario for Farm Planning in Deli Serdang

Abstract

This study examines a calculus-based production scenario intended to support discussion of rice-farm planning in Deli Serdang, Indonesia. A deterministic simulation integrates an assumed accumulation rate of 20 + 3t over a 120-day crop cycle, where time is measured in days. The resulting function is Q(t) = 20t + 1.5t², giving a modeled cumulative quantity of 24,000 kg at day 120. At an assumed price of IDR 5,500 per kg, this quantity corresponds to gross revenue of IDR 132,000,000. The positive second derivative describes a convex quadratic trajectory; it does not demonstrate exponential growth, increasing returns to farm inputs, or improvements in soil fertility. The coefficients were not calibrated against documented field measurements, and the cultivated area, production costs, and conversion from biomass to marketable grain were not specified. Consequently, the calculation is an illustrative scenario rather than a validated harvest forecast or a profitability assessment. Extending the same trajectory across successive harvest cycles is not justified. The example can help explain accumulation and the distinction between revenue and profit, while practical application requires local yield measurements, explicit area