LINEAR PROGRAMMING PROBLEM: SOLVING PROBLEMS ABOUT SOLUTIONS AND THEIR PROPERTIES
DOI:
https://doi.org/10.55640/Keywords:
Linear programming; optimization models; feasible region; extreme point; simplex method; optimal solution; degeneracy; duality; constraint analysis; mathematical optimization.Abstract
This article examines problem-solving approaches for linear programming with a specific focus on the structure of feasible solutions and the analytical properties that determine optimality. The study systematizes classical and modern methods used to solve linear programming problems, including geometric interpretation, simplex-based procedures, and analytical verification of solution validity. Particular attention is given to the characterization of feasible regions, boundary behavior, extreme points, and the conditions under which optimal solutions exist or become degenerate or multiple. Through representative problem cases, the paper demonstrates how theoretical properties influence algorithmic performance and decision-making accuracy in practical applications. The discussion emphasizes logical rigor in modeling, sensitivity to constraints, and the interpretation of solution sets within real optimization contexts. The results contribute to a clearer understanding of how structural properties of linear models guide both solution selection and evaluation, offering a coherent framework suitable for educational, analytical, and applied optimization tasks.
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