Keiser University - Institutional RepositoryInterpretable Quadratic Cost Functions for Data-Driven Manufacturing: A Finite-Difference, Calculus-Based Framework Integrating Economic Theory and Explainable Business AnalyticsLauraCruz TreminioauthorThis study develops a mathematically rigorous, five-stage quadratic cost-modeling framework using seven years of real production data (2015–2021). By integrating finite-difference numerical analysis with differential calculus and microeconomic theory, the deductive-empirical architecture maintains full mathematical transparency over opaque "black-box" machine learning algorithms. The estimated quadratic model captures initial economies of scale through declining marginal costs, and while its predictive accuracy diminishes in later periods due to unmodeled structural shifts, this limitation explicitly serves as a diagnostic tool to highlight model boundaries. Ultimately, the authors contribute a fully replicable, FAIR-aligned pipeline that successfully unifies discrete numerical methods with continuous cost theory to advance explainable business analytics and managerial decision-making. --------------------- Este estudio desarrolla un marco de modelado de costos cuadrático de cinco etapas, matemáticamente riguroso, utilizando datos de producción reales de siete años (2015-2021). Al integrar el análisis numérico de diferencias finitas con el cálculo diferencial y la teoría microeconómica, la arquitectura deductivo-empírica mantiene una total transparencia matemática sobre los opacos algoritmos de aprendizaje automático de "caja negra". El modelo cuadrático estimado captura las economías de escala iniciales mediante la disminución de los costos marginales, y si bien su precisión predictiva disminuye en períodos posteriores debido a cambios estructurales no modelados, esta limitación sirve explícitamente como una herramienta de diagnóstico para resaltar los límites del modelo. En definitiva, los autores aportan un proceso totalmente replicable y alineado con los principios FAIR que unifica con éxito los métodos numéricos discretos con la teoría de costos continuos para impulsar el análisis empresarial explicable y la toma de decisiones gerenciales.Production. Theory of the firm. Supply-side economics [HB241]Mathematical models [HD30.25]Manufactures [TS]Keiser University Latin American Campus, San Marcos, NicaraguaMonograph

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