Methods and systems for minimizing the power consumed by a supercharger pump in an engine system. The methods and systems minimize the delta pressure across the pump with a control strategy for positioning the electronic throttle and supercharger bypass valve in a coordinated manner to deliver the required amount of fresh air flow into engine (i.e., the air flow associated with the driver's requested torque), while, at the same time, minimizing the power consumed by the supercharger pump for best fuel economy.