With the ongoing climate crisis, supporting a sustainable future has been a priority worldwide. Generating power that does not produce greenhouse gas emissions and reducing the dependence on imported fuel sources made the use of renewable energy resources skyrocket in recent years. Wind energy specically is one of the fastest growing renewable energy resources. In this study, we answer important mathematical questions in the development of a wind project. We compare various analytical models to better understand the wake created by a turbine, and how the wake-interaction within a wind farm affects overall energy production. With a better understanding of wake modeling, we further analyze how the various wake models affect the wind farm layout optimization problem, with the goal of minimizing wake interaction and therefore maximizing energy production. These results are important to consider when developing a wind project because they govern the overall nancial viability of a potential wind farm.