On the basis of the theory of irreversible thermodynamics and an elementary model of the molecular motors converting chemical energy by ATP hydrolysis to mechanical work exerted against an external force, the efficiencies of the molecular motors at two different optimization configurations for trade-off figure of merit representing a best compromise between the useful energy and the lost energy are calculated. The upper and lower bounds for the efficiency at two different optimization configurations are determined. It is found that the optimal efficiencies at the two different optimization configurations are always larger than 1/2. (C) 2017 Elsevier B.V. All rights reserved.