This paper presents the modeling and analysis of a bypass mixing tank process with non-minimum phase behavior. The presence of a bypass line introduces a right-half-plane (RHP) zero, leading to inverse response behaviour that complicates control. The process is modeled as a first-order non-minimum phase system with a stable pole and a right-half-plane zero. The time response is analyzed for three different ratios of the zero-time constant to the process time constant. To further examine the effect of the bypass ratio (α), four operating scenarios are considered: no bypass (α = 0), moderate bypass (α = 0.3), high bypass (α = 0.6), and extreme bypass (α = 1.5). Each scenario yields distinct dynamic behaviour due to variations in bypass flow, process gain, and time constants. The corresponding transfer functions are derived to illustrate how an increase in bypass ratio enhances the inverse response and slows down the system dynamics. This work develops a simple dynamic model for the bypass mixing tank using a first principles-based FONMP approach and compares different PI control methods for various bypass ratios. The analysis provides valuable insights into how bypass flow affects system performance, laying a foundation for future control design of non-minimum phase processes.