Capturing CO2 directly from air is one of the options for mitigating the effects global climate change, and therefore determining its cost is of great interest. A process model was proposed and validated using laboratory results for adsorption/desorption of CO2, with a branched polyethyleneimine (PEI) loaded mesocellular foam (MCF) silica sorbent. The model was subjected to a Multi-Objective Optimization (MOO) to evaluate the technoeconomic feasibility of the process and to identify the operating conditions which yielded the lowest cost. The objectives of the MOO were to minimize the cost of CO2 capture based on a discounted cash flow analysis, while simultaneously maximizing the quantity of CO2 captured. This optimization identified the minimum cost of capture as 612 USD tonne−1 for dry air entering the process at 25 °C, and 657 USD tonne−1 for air at 22 °C and 39% relative humidity. The latter represents more realistic conditions which can be expected for subtropical climates. The cost of direct air capture could be reduced by ~42% if waste heat was utilized for the process, and by ~27% if the kinetics of the sorbent could be improved by a factor of two. A combination of both would allow cost reductions of ~54%.