The [hmim][Tf2N] ionic liquid is considered in this work to develop a model in Aspen Plus® capturing carbon dioxide from shifted flue gas through physical absorption. Ionic liquids are innovative and promising green solvents for the capture of carbon dioxide. As an important aspect of this research, optimization is carried out for the carbon capture system through a central composite design: simulation and statistical analysis are combined together. This leads to important results such as the identification of significant factors and their combinations. Surface plots and mathematical models are developed for capital costs, operating costs and removal of carbon dioxide. These models can be used to find optimal operating conditions maximizing the amount of captured carbon dioxide and minimizing total costs: the percentage of carbon dioxide removal is 93.7%, operating costs are 0.66 million €/tonCO2 captured (due to the high costs of ionic liquid), and capital costs are 52.2 €/tonCO2 captured.