by Prasham Patel
Project Outcome: Mini research paper
Project Description: Prasham’s project focused on using the Cobb-Douglas production function and Lagrangian multipliers to determine the most cost-effective production strategy for his father’s firm. The Internal Assessment, completed over two months, involved applying advanced mathematical concepts to model and optimize the firm’s cost of production.
Using the Cobb-Douglas function, Prasham was able to model the firm’s production cost function, considering the relationship between the inputs used in production. Through mathematical manipulations and Lagrangian functions, he utilized partial derivatives to minimize production costs while meeting a specified production target. Additionally, Prasham employed profit optimization techniques for the firm, incorporating the specific production function to identify the most efficient and cost-effective approach.
This project, which was a part of the DP Math AA HL course, showcased Prasham’s ability to apply complex mathematical tools, such as the Cobb-Douglas function and Lagrangian multipliers, to real-world business scenarios, demonstrating a deep understanding of both mathematical theory and its practical applications in economics.