Method and system for controlling a compressor and a supply fan in a heating, ventilating and air conditioning (HVAC) system are disclosed. The system includes a compressor having a startup state and a running state, a supply fan, and a controller configured to control the compressor and the supply fan in the HVAC system. The compressor and the supply fan are controlled based on a dehumidification map and/or an efficiency map. The system also includes a cooling coil configured to receive a fluid in heat exchange relationship with refrigerant from an evaporator to cool air. The supply fan is configured to deliver the cooled air from the cooling coil to a conditioned space as supply air.