This document describes advanced simplex methods—Big M and Two Phase—for solving LPPs with ≥ or = constraints. Outlines the use of artificial variables for infeasible starts, assigns penalty parameters, and details stepwise solutions using both methods with case studies, clarifying approaches for complexities in linear programming.
Explains the core concepts of the simplex algorithm for solving LPPs. Focuses on its iterative process, starting from an initial solution and navigating toward optimality using a structured tableau and pivoting strategy. Demonstrates application through practical examples and highlights conditions for algorithm use.
Covers various mathematical forms of linear programming problems: general, matrix, canonical, and standard. Explains constraints, slack and artificial variables, and standardization required for simplex analysis. Outlines the terminology and stepwise preparation of LPPs for algorithmic optimization methods
Explores the graphical method for solving linear programming problems with two decision variables. Presents a step-by-step approach—formulating, graphing constraints, defining feasible region, and pinpointing optimal solution. Discusses special cases, multiple solutions, and interpreting graph results, preparing students for visual analysis in LPP scenarios.
Introduces operations research, its systematic application to managerial problems, and foundational aspects of linear programming. Covers LPP definitions, components, basic assumptions, and methods of problem formulation. Demonstrates with real-life examples on maximizing profits, minimizing costs, and optimal resource allocation, equipping readers with essential tools for quantitative decision-making.