Linear Programming: Solving Optimization Problems Graphically

Do you need to make optimal decisions when faced with limited resources and constraints? Linear Programming (LP) is the fundamental mathematical tool used across business, logistics, and engineering to solve complex optimization challenges. This course provides a complete, text-based introduction to the principles of Linear Programming. By the end, you will be able to model real-world resource allocation scenarios, define objective functions and constraints, and find optimal solutions using the powerful graphical method. What you'll learn: * Understand the core components of a Linear Programming model, including objective functions, decision variables, and constraints. * Practice formulating real-world optimization challenges into standard two-variable LP models. * Master the graphical technique for identifying the feasible region and finding the optimal vertex solution. * Apply sensitivity analysis to interpret how changes in resource availability affect the optimal outcome. * Identify and interpret special cases in LP, such as unbounded solutions, multiple optimal solutions, and infeasible regions. The course begins with foundational terminology and modeling principles before moving step-by-step through the process of graphing inequalities, defining the feasible region, and calculating the optimal solution. Practical exercises reinforce the understanding of constraint interaction and boundary analysis. This course is designed for absolute beginners in optimization and mathematical modeling. No prior knowledge of linear programming is required, only a basic familiarity with algebra and plotting linear equations. Start mastering the mathematical foundation of optimization today.