This paper suggests a method for optimal power assignment of the satellite transponder input carriers in the Multi-level & Multi-bandwidth system. The interference and the noise effects analyzed for the optimal power assignment are intermodulation product caused by the nonlinear transponder characteristics, adjacent channel interference, co-channel interference, and thermal noise in the satellite link. The Fletcher- Powell algorithm is used to determine the optimal input carrier power. The performance criteria for optimal power assignment is classified into 4 categories according to the CNR of destination receiver earth station to meet the requirement for various satellite link environment. We have performed mathematical analysis of objective functions and their derivatives for use in the Fletcher-Powell algorithm, and presented various simulation results based on mathematical analysis. Since the satellite link, it is meaningful to model and analyze these effects in a unified manner and present the method for optimal power assignment of transponder input carriers.