Managing fragile island freshwater resources requires identifying pumping strategies that trade off the financial cost of groundwater supply against controlling the seawater intrusion (SWI) associated with aquifer pumping. In this work, these tradeoffs are investigated through a sensitivity analysis conducted in the context of an optimization formulation of the groundwater management problem, which aims at minimizing the groundwater supply operation cost associated with groundwater pumping and desalination treatment, subject to constraints on SWI control, as quantified by the water table drawdown over the well (∆s), the reduction in freshwater volume (∆FV) in the aquifer, or the salt mass increase (∆SM) in the aquifer. This study focuses on a simplified two‐dimensional model of the San Salvador Island aquifer (Bahamas). Pumping strategies are characterized by the distance of the pumping system from the shoreline (WL), the abstraction screen depth (D) and overall pumping rate (Q), constituting the decision variables of the optimization problem. We investigate the impacts of pumping strategies on the operation cost, ∆s, ∆FV and ∆SM. Findings indicate increasing D or decreasing WL reduces ∆s, ∆FV and ∆SM, thus preserving the aquifer hydrogeologic stability, but also leads to extracting saltier groundwater, thus increasing the water treatment requirements, which have a strong impact on the overall groundwater supply cost. From a financial perspective, groundwater abstraction near the island center and at shallow depths seems the most convenient strategy. However, the analysis of the optimization constraints reveals that strategies where the pumping system approaches the island center tend to cause more severe SWI, highlighting the need to trade off groundwater supply cost against SWI control.