What mathematical technique is used for solving optimization problems through linear functions under certain constraints?

Linear programming is a mathematical technique specifically designed for solving optimization problems where both the objective function and the constraints are linear functions. This approach allows decision-makers to determine the optimal allocation of resources while adhering to specified limitations.

In linear programming, the goal is typically to maximize or minimize a linear objective function, subjected to a set of linear inequalities or equalities representing the constraints. This makes linear programming particularly useful in various fields such as economics, engineering, and logistics, where optimizing resources is essential.

The technique relies on methods such as the Simplex algorithm or graphical methods to find the best solution at the vertices of the feasible region defined by the constraints. Its application can range from planning production schedules to optimizing transportation routes and resource allocations.

Other options, while also involving optimization techniques, do not align with the strict linearity criteria of the problem described. For instance, integer programming deals with problems that require some or all variables to be integers, dynamic programming addresses problems where solutions can be broken into simpler subproblems, and quadratic programming involves an objective function that is quadratic in nature, not linear. Thus, linear programming stands out as the correct answer in the context of the question.