The Simplex method is a mathematical technique used for solving linear programming problems. It helps find the best possible outcome, such as maximizing profit or minimizing costs, given a set of linear constraints. The method operates on a feasible region defined by these constraints and iteratively moves towards the optimal solution. Developed by George Dantzig in the 1940s, the Simplex method uses a tabular approach to evaluate corner points of the feasible region. By systematically testing these points, it identifies the one that yields the best value for the objective function, ensuring efficient resource allocation in various fields like economics and engineering.