In this paper, we assess the performance of a boundary layer ingesting turboelectric aircraft configuration for commercial transport. The analysis is carried out by casting the relations governing the sizing and performance of the aircraft system as an optimization problem. The objective and constraint functions are defined such that the model can be formulated as a signomial program (SP) and solved with an existing toolkit using robust geometric programming (GP) solution methods. The framework allows the aircraft to be described as a collection of SP-compatible component models which are optimized simultaneously, including the effect of system-level interaction between components. Predicted configuration sizing and performance of the distributed turboelectric propulsion configuration are comparable to that of an equivalent conventional configuration baseline. Sensitivities of fuel burn to input parameters are outputs of the solution and provide insight into the quality of both the initial selection of design parameters and the model formulation. Optimization of the aircraft and propulsion system demonstrates the usefulness of a global optimization framework for addressing multi-disciplinary challenges in electrified aircraft propulsion system design.