The correct answer is A) opens the burner circuit upon sensing a flame failure. A photoelectric cell installed in an automatically fired auxiliary boiler burner management system is designed to detect the presence of a flame and open the burner circuit if the flame is lost. This is a safety feature to shut off the fuel supply and prevent a potential fire or explosion hazard. The other options are incorrect because: B) a photoelectric cell does not directly detect radiant heat, C) the photoelectric cell operates the burner circuit electronically without mechanical linkage, and D) the photoelectric cell must be operational at all firing rates to maintain proper safety controls.