The Markowitz mean-variance model is an important tool in portfolio theory. This study examines the complexity of the model by analyzing its application and performance under different constraints. The study uses Bloomberg data on 10 stocks from 2001 to 2021 to rigorously analyze the impact of limitations on portfolio optimization. The study explores limitations ranging from limiting total allocations and individual weightings to intentional exclusions and long-term strategies to discern the impact on the risk-reward profile. The research uses graphical representations and key metrics such as Sharpe ratios, stock allocation lines, and various portfolio metrics to provide insight into optimal allocation strategies. The results indicate that these constraints have a significant impact on the risk-return profile of a portfolio and that it is essential to take them into account when optimizing a portfolio. The study provides a comprehensive analysis of the Markowitz model and its application under various constraints, which can help investors make informed decisions while optimizing their investment portfolios.