The paper presents an economic optimization of a STHX with two commonly adopted (i.e., Kern and Bell-Delaware) and one rarely explored (i.e., Wills-Johnston) methods. A detailed numerical code concerning thermal, hydraulic, exergy, and economic analysis of STHX is developed for all three methods. Normalized sensitivity analysis, parametric study, and Genetic Algorithm are used to ascertain the most influential parameters and optimize the total cost. It is observed that the calculations made using the Wills-Johnston method were reasonably close to the Bell-Delaware method. While the Kern method showed a significant deviation in the shell side calculations because of the several assumptions in this method. The parametric analysis showed that increasing the mass flow rate and the number of baffles increased the operating cost because of an exponential increase in the pressure drops. Finally, the optimization reduced the heat transfer area by ~26.4%, capital cost by ~20%, operational cost by ~50%, total cost by ~22%, and the stream cost by ~21%.