Exploring Lagrangian Optimization

This repository contains the final project I completed for a high school multivariable calculus course. The goal was to study constrained optimization through self-directed research, produce a written report, and present the material to the class.

The paper is not intended for formal journal publication, it instead documents our learning and presentation materials.

Project focus:

• Topic: constrained optimization using Lagrange multipliers
• Approach: derive the theory, work through worked examples, compare methods
• Examples included: Cobb-Douglas optimization (economics), a constrained physics problem, and classroom-friendly demonstrations

Contents and artifacts

• Paper: LaTeX source in paper/ and compiled PDF at paper/wrapper.pdf.
• Presentation: slides and web presentation in presentation/ (HTML + source). The slide sources live in presentation/ and presentation/template.html is the template.
• References and notes: paper/references/ and paper/sections/ contain supporting material and section files.

Build & usage notes

• Build the paper (requires a TeX distribution such as TeX Live or MiKTeX):

latexmk -pdf paper/wrapper.tex

or run pdflatex / bibtex as needed until references compile.

• Serve or build the slides (from manim-slides):

manim-slides convert Introduction Lagrange_Multipliers Key_Differences Cobb_Douglas_Introduction Cobb_Douglas_Problem Physics_Problem main.html --use-template template.html