A method for optimizing the design of a fusion reactor blanket as a function of several design variables is applied to a modified version of the HYLIFE inertial confinement fusion reactor. This reactor concept uses an inner liquid lithium blanket for breeding tritium and an outer manganese-steel blanket to increase the fusion energy multiplication factor. The capital cost per unit of net electric power produced is minimized subject to constraints on the tritium breeding ratio and the radiation damage rate in the first structural wall. The optimal design has a 0.9-m-thick lithium blanket denatured to 0.1 % 6Li.