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Urban vertical farming has emerged as a sustainable and innovative approach to addressing the increasing global demand for food in rapidly growing and densely populated cities, where traditional agriculture faces significant challenges due to space and resource constraints. A primary issue in these systems is the efficient management of critical resources, particularly water and energy, which are essential for maintaining high crop productivity and environmental sustainability. This study introduces, develops, and evaluates a mathematical model that integrates Internet of Things (loT) technology to optimize water and energy usage in a hydroponic vertical farming setup. The model utilizes real-time environmental data collected from loT sensors to dynamically adjust irrigation and energy consumption, ensuring minimal waste while sustaining optimal conditions for plant growth. Extensive simulations conducted using Python demonstrate substantial improvements in Water Use Efficiency (WUE) and significant energy savings, validating the model's effectiveness. The study also presents practical case studies from regions like Singapore, Qatar, and Malaysia, showcasing how the integration of renewable energy sources, such as solar photovoltaic panels, with advanced smart irrigation technologies can lead to up to 50% growth rate improvements. Despite existing challenges, such as high initial capital investments, technical complexities, and the need for continuous maintenance, the findings indicate that modular and scalable system designs offer a promising path forward. Future research should aim to reduce overall costs and enhance system adaptability for various urban environments. Ultimately, this research provides a scalable and efficient framework for advancing urban agriculture, with the potential to contribute significantly to global food security and promote the sustainability of urban ecosystems. [ABSTRACT FROM AUTHOR]