This analysis has demonstrated that fundamental mathematical constructs—from basic functions to partial derivatives and constrained optimization—provide a rigorous and indispensable framework for modern economic analysis. These tools allow us to move beyond conceptual theory to build quantitative models of complex business scenarios. Functions define the core relationships between costs, revenues, and market forces. Differential calculus enables dynamic analysis, allowing for the optimization of outcomes through marginal analysis and the measurement of sensitivity through concepts like elasticity. Finally, multivariate and constrained optimization methods, such as the use of Lagrange multipliers, equip decision-makers to allocate scarce resources in the most efficient way possible. Ultimately, these mathematical tools empower economists and business leaders to model complex scenarios, optimize strategic outcomes, and make informed, data-driven decisions.