Multivariable Calculus for Econ — Helio Verde Three-Product Optimisation

Run Helio Verde Beverages' three-product portfolio (Cola, Agua, Sport) through the full multivariable-calculus apparatus: gradients on the unconstrained surface (Round 1), the constrained Lagrangian with KKT conditions and shadow prices for bottling, sugar and labour (Round 2), and the envelope theorem with comparative statics for scenario analysis under a sugar-price shock (Round 3). Designed for advanced undergraduate methods courses, Master's-level quantitative-methods modules, and exec-ed cohorts of CFOs and OR practitioners with prior calculus.