The Robeson correlation is an empirical plot that shows a tradeoff between selectivity and permeability of gases whose upper boundary is often used to evaluate the performance of a membrane system. This work shows that it is possible to define an optimum permeability/selectivity point on this boundary based on economic optimization. Examples are presented for the separation of four gas pairs: CO2/N2, O2/N2, CO2/CH4, and N2/CH4. The constraints used to limit the optimal point are based on the cost of the membrane, the number of units required to achieve a specific separation, and the compression requirements. The total costs include the fees for utilities and capital costs, and interest payments. The model results are verified against other studies, while initial and targeted parameters are subject to a sensitivity analysis. The optimum points obtained at an operating pressure of 1 MPa were for CO2/N2 a permeability of 3200 barrers and a selectivity of 24, for O2/N2 a permeability of 550 barrers and a selectivity of 4, for CO2/CH4 a permeability of 2000 barrers and a selectivity of 20, and for N2/CH4 a permeability of 110 barrers and a selectivity of 2. A wide range of permeability and selectivity requirements exist for a separation, which depend on a particular gas pair.