Operations research is a scientific approach to decision making that seeks to optimize systems with scarce resources. It uses mathematical modeling to formulate and solve problems. The methodology involves formulating the problem, developing a mathematical model, deriving a solution from the model, selecting alternatives, validating the model, implementing and evaluating recommendations. Linear programming is an optimization technique that finds optimal values for decision variables in an objective function subject to constraints. It involves writing decision variables, formulating the objective function and constraints, and adding non-negativity constraints.