Scramjets are a class of hypersonic airbreathing engine that are associated with realizing the technology required for economical, reliable and high-speed access-to-space and atmospheric transport. The expanding flow in the scramjet nozzle comprises of unburned hydrogen which under ideal conditions, can be utilized to introduce an after-burning scheme. After-burning augments the thrust produced by the scramjet nozzle and creates a more robust nozzle design. This paper presents a single-objective design optimization considering three design variables with the objective of producing maximum thrust augmentation. It is found that significant levels of thrust augmentation are produced based upon contributions from increased pressure, mass flow and energy in the nozzle. Further understanding of the phenomenon by which thrust augmentation is being produced is provided in the form of variance-based global sensitivity analysis, force contribution breakdowns, analysis of the nozzle flowfields, analysis of the surface pressure and shear stress distributions acting on the nozzle wall and analysis of the combustion efficiency.