DESIGN AN INTERACTIVE SOFTWARE APPLICATION THAT WILL HELP TO CONSTRUCT EQUATIONS OF LINEAR PROGRAMMING AND DIOPHANTINE EQUATIONS USING ORACLE AI AGENTS TO ARRIVE AT KEY MANUFACTURING DECISIONS

Abstract

Manufacturing organizations face increasingly complex optimization challenges that require sophisticated mathematical modeling capabilities. This research presents the design of an interactive software application that leverages Oracle AI agents to construct Linear Programming and Diophantine equations for critical manufacturing decisions. Traditional optimization approaches demand specialized mathematical expertise, creating barriers for operational managers who understand production constraints but lack advanced mathematical training. Our proposed application bridges this gap by employing AI agents that translate business requirements into mathematical formulations automatically. The system interprets natural language descriptions of manufacturing constraints, resource limitations, and optimization objectives, then constructs appropriate Linear Programming models for continuous optimization and Diophantine equations for discrete decision scenarios. Through intelligent agent architecture, the application validates mathematical consistency, suggests constraint refinements, and provides scenario analysis capabilities. The research demonstrates how Oracle AI integration enables real-time optimization that adapts to changing manufacturing conditions. This work contributes both theoretical frameworks for AI-assisted mathematical modeling and practical applications for manufacturing decision support systems that democratize access to advanced optimization techniques.