We investigate the radial displacement of a viscous fluid inside a horizontal circular Hele-Shaw cell, driven by the injection of a less viscous fluid at the center of the cell. We compare how different injection protocols affect the instability of the interface between the two fluids and the displacement efficiency of the system. Such injection protocols are modeled as linear-plateau functions of time, which start from a null injection rate, and increase this injection rate linearly in time, until it reaches a plateau. This constant value emulates the maximum possible injection rate in an industrial oil production system that utilizes fluid injection into the reservoir as an improved oil recovery method. The numerical simulations that track the evolution of viscous fingering in the interface stop when they reach a predetermined radial distance, analogous to the distance between the injection and production wells. Results show that lower injection rates tend to generate a reduced number of viscous fingers, which have smaller amplitudes, consequently leading to greater displacement efficiencies. This allows for more volume of the less viscous fluid to be injected into the cell, before the predetermined radius distance is reached. On the other hand, lower injection rates require longer injection times, which translates into additional operational costs in an oilfield operation. We therefore present a strategy to optimize the linear-plateau injection protocol that maximizes profit, aiming at an increase of displacement efficiency, while also considering the losses of time and related increases in operational costs.