2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64335We present a simple geometric construction for smoothing polyhedral utility functions. Keywords: Afriat- Varian theorem, the utility function, the economic indices theory, convex analysis.LATeX2e, 4 pagesOptimization and ControlMetric Geometry91B42, 91B16 (Primary) 90C25 (Secondary)text