Solving Optimization Problems Using the Graphical Method of Linear Programming

Year : 2025 | Volume : 14 | Issue : 02 | Page : 01 08
    By

    Sakshi Saxena,

  • Vainesh Solanki,

  • Gooty Rohan,

  1. Researcher, Ajeenkya D Y Patil University (SOE), Charholi Budruk, Pune, Maharashtra, India
  2. Researcher, Ajeenkya D Y Patil University (SOE), Charholi Budruk, Pune, Maharashtra, India
  3. Professor, Ajeenkya D Y Patil University (SOE), Charholi Budruk, Pune, Maharashtra, India

Abstract

Linear programming is a mathematical optimization technique used for maximizing or minimizing a linear objective function while satisfying a set of linear constraints. This method plays a crucial role in various industries, including manufacturing, finance, transportation, and supply chain management. Among the different approaches to solving linear programming problems, the graphical method provides a simple and intuitive way to visualize and solve problems involving two decision variables. By plotting constraints on a Cartesian plane, the method allows for the identification of feasible regions and optimal solutions through geometric interpretation. Although limited to two-variable cases, it serves as an effective educational tool for understanding the fundamental principles of optimization. The graphical method follows a structured approach involving the formulation of an objective function, plotting constraints, determining the feasible region, and evaluating the objective function at the corner points. By analyzing these corner points, the optimal solution can be determined efficiently. This paper presents a step-by-step explanation of the graphical method, supplemented by a case study demonstrating its practical application in a real-world scenario. The study illustrates how businesses can utilize this method to maximize profits, minimize costs, and allocate resources efficiently. Despite its simplicity and effectiveness, the graphical method has limitations, such as its inability to handle problems with more than two decision variables. For larger and more complex problems, alternative approaches such as the simplex method or computational optimization tools are required. Nonetheless, the graphical method remains a valuable tool in operations research, providing foundational knowledge for more advanced linear programming techniques. This paper also discusses the advantages, disadvantages, and applications of the graphical method across various fields, reinforcing its importance in decision-making and optimization strategies.

 

Keywords: Linear programming, graphical method, optimization, feasible region, objective function, constraints, operations research.

[This article belongs to Research & Reviews : Journal of Statistics ]

How to cite this article:
Sakshi Saxena, Vainesh Solanki, Gooty Rohan. Solving Optimization Problems Using the Graphical Method of Linear Programming. Research & Reviews : Journal of Statistics. 2025; 14(02):01-08.
How to cite this URL:
Sakshi Saxena, Vainesh Solanki, Gooty Rohan. Solving Optimization Problems Using the Graphical Method of Linear Programming. Research & Reviews : Journal of Statistics. 2025; 14(02):01-08. Available from: https://journals.stmjournals.com/rrjost/article=2025/view=211758


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Regular Issue Subscription Review Article
Volume 14
Issue 02
Received 28/01/2025
Accepted 11/04/2025
Published 30/05/2025
Publication Time 122 Days
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