With both engine run switches off, what EICAS message should appear if both fuel pumps are in automatic mode and the APU knob is selected to RUN?

When both engine run switches are off and the APU knob is selected to RUN, the EICAS (Engine Indication and Crew Alerting System) will indicate the status of the fuel pumps in response to the activated APU. In this scenario, if both fuel pumps are in automatic mode, the system is designed to automatically activate the fuel pumps necessary to supply fuel to the APU.

The appearance of the message "Cyan R FUEL PUMP ON (A)" signifies that the right fuel pump is engaged and functioning properly to ensure fuel flow to the APU. The cyan color indicates that this message is for information purposes and is not critical, reflecting that the system is performing as intended.

The other options do not accurately describe the expected EICAS message under these conditions. The left fuel pump would not specifically prompt a separate line in the EICAS if both pumps are functioning, and messages regarding fuel pumps being inoperative or the APU running would display under different circumstances. Therefore, the presence of "Cyan R FUEL PUMP ON (A)" confirms that the system is working correctly and supplying the necessary fuel for APU operation while both engine run switches are off.