The global demand for high-quality sheep meat and goat meat has driven innovations in breeding strategies to enhance productivity and profitability. Back-crossing, a selective breeding technique, has emerged as a promising approach to gaining desirable traits while maintaining genetic integrity. This study investigates the application of mathematical models to understand back-crossing strategies in goat breeding, focusing on maximizing meat yield and quality of goat meat. Using a combination of deterministic modeling and macro genetics principles, we developed a framework to predict the inheritance patterns of the overall key traits. Preliminary results demonstrate that a mathematical model can significantly enhance the understanding of outcomes of back-crossing programs. For instance, simulations suggest that strategic selection of back-crossing parental lines is needed to accelerate the introgression of target traits, compared to conventional inter-filial breeding methods. Furthermore, the inclusion of economic factors ensures the feasibility of these improvements for commercial application. This study highlights the potential of mathematical tools to revolutionize goat breeding practices, offering a scientific basis for decision-making in agricultural systems. The findings provide actionable insights for breeders and policymakers, paving the way for sustainable and efficient meat production.