Analysis of practical applications using the linear programming model

Abstract

A linear programming model is a mathematical optimization technique used to find the best possible outcome in a mathematical model with linear relationships under a set of constraints. This technique has various applications in engineering, management, economic analysis, and military operations. The linear programming model is the most popular technique for determining the best course of action, and it is essential for decision-making and resource allocation in modern society. This research paper will introduce the standard form of the linear programming model and explore the differences and solutions between three linear programming models: 0-1 integer programming, mixed integer programming, and multi-objective programming. In the case of introducing the application and optimization effect of different models in real life, list research and compare the different applications and research scenarios of the three models to derive the strengths, weaknesses, and characteristics of the different models to achieve the effect of providing more targeted models for different real-life cases.