Which mathematical technique optimizes an objective function subject to constraints?

The correct answer is linear programming, as it specifically focuses on optimizing an objective function while considering various constraints. In linear programming, the objective function typically involves maximizing or minimizing a value—such as profit or cost—using linear relationships. The constraints are formulated as linear inequalities or equations, which define the feasible region within which a solution must lie.

Linear programming is widely applied across diverse fields such as finance, logistics, manufacturing, and marketing, allowing practitioners to make optimal decisions under given limitations. It employs methods such as the Simplex algorithm or graphical methods to find the best possible outcome based on the provided constraints.

While simulation is a valuable technique for analyzing complex systems, it does not directly optimize the objective function within constraints. Instead, it models various scenarios to understand potential outcomes. Queuing theory focuses on analyzing waiting lines and does not specifically deal with optimizing an objective function, and operations research encompasses a broader range of techniques beyond just linear programming, including statistical methods and decision analysis. Nonetheless, within the context of the question, linear programming distinctly stands out as the technique designed for optimization under constraints.