feasible solution

Optimization is a field of mathematics focused on finding the best possible solution to a problem, given a set of constraints. This often involves maximizing or minimizing a specific objective function. For example, a factory might want to maximize profit (the objective function) by deciding how many of two products to make, subject to limitations on raw materials, machine time, and labor (the constraints).12

A key concept is the "feasible solution," which represents any combination of variables that satisfies all the given constraints. In linear programming, a common type of optimization, the goal is to find the optimal values for variables within a defined region of possible solutions. The simplex method, developed by George Dantzig, is an efficient algorithm used to solve these problems, especially when dealing with many variables and constraints.345