Application of ChatGPT in Solving Lagrangian Multiplier Problems by Deductive Reasoning

Abstract

This paper investigates the potential of ChatGPT to solve constrained optimization problems in economic mathematics using the Lagrangian multiplier method. By applying a deductive reasoning framework, we examine whether ChatGPT can derive unknown values step by step from given data using known mathematical formulas. We also propose a prompt strategy that enables ChatGPT to generate deductive reasoning process graphs, allowing visualization of its logical steps. Our case studies show that ChatGPT often provides correct solutions and interpretations of the Lagrange multiplier <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\lambda$</tex>, especially when problems follow familiar patterns. However, two significant limitations remain: ChatGPT does not fully grasp the mathematical meaning of expressions and frequently struggles with problems requiring structured case analysis. Despite these challenges, reasoning graphs and carefully crafted prompts offer educators a useful way to clarify the Artificial Inteligent's (AI) internal logic. ChatGPT can be a valuable educational assistant, provided human oversight and prompt engineering are appropriately applied

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