Optimizing Resource Allocation: A Comprehensive Analysis of Linear Programming Formulations and Solution Methods

Abstract

Linear Programming Problem (LPP) is also known as Linear Optimization. It is one of the simplest and most used techniques of operations. LPP is widely used in the fields of economics, operation research, finance, decision making and resource allocation optimization. LPP is used in different scenarios, where the relations of variables and objective functions is linear and constant. It maximizes or minimizes the given function of variable. This research paper delves into the realm of Linear Programing Problems, focusing on the formulation of Mathematical Models for various scenarios and exploration of different solution methods. The most common methods to solve the LPP are Graphical method, Simplex and the use of Excel Solver. These solutions provide the Initial basic feasible solution and the optimal solution also. The study aims to provide a comprehensive understanding of how LPP can be effectively applied to optimize resource allocation in different contexts.