Mathematical optimization is a crucial field that focuses on finding the best possible solutions from a range of options. At its essence, optimization involves maximizing or minimizing a specific goal while considering various constraints or limitations. This process is widely applicable across many areas, including business, engineering, healthcare, and logistics. The optimization process starts by defining the problem clearly, identifying the key variables involved, and understanding the constraints that may impact the potential. One of the most common methods used in this field is linear programming, which involves problems where both the goals and constraints are expressed as linear relationships. This approach is particularly useful for tasks like resource allocation, where the objective is to use limited resources in the most efficient way. In contrast, nonlinear programming deals with problems that involve complex relationships between variables, allowing for a wider range of potential solutions.