The placement of wind turbines is a crucial design element in wind farms, given the energy losses resulting from the wake effect. Despite numerous studies addressing the Wind Farm Layout Optimization (WFLO) problem, considering multiple directions to determine wind turbine spacing and layout remains limited. However, relying solely on one predominant direction may lead to overestimating energy production, and loss of energy generation. This work introduces a novel mathematical programming optimization framework to solve the WFLO problem, emphasizing the wind energy's nonlinear characteristics and wake effect losses. Comparisons with traditional layout approaches demonstrate the importance of optimizing wind farm layouts during the design phase. By providing valuable insights into the renewable energy sector, this research aims to guide future wind farm projects towards layouts that balance economic considerations with maximizing energy production.