An irreversible hybrid molten carbonate fuel cell-Braysson heat engine is taken into account. Basic thermodynamics parameters including power output, efficiency and exergy destruction rate are considered. In addition ecological function and new criteria, which is based on ecological function, for heat engines called as modified ecological function is suggested. Optimum conditions for mentioned parameters above are determined. Numerical results are obtained and plotted. Finally, results are discussed. (C) 2016 Elsevier Ltd. All rights reserved.