The adsorption isotherms of both naproxen enantiomers were measured on a (R,R)-Whelk-O1 chiral adsorbent from a mobile phase made of liquid carbon dioxide and methanol, using frontal analysis. These isotherms were used to model the competitive adsorption behavior of a racemic mixture of naproxen enantiomers. Their overloaded elution band profiles were calculated numerically using these isotherm data. The injected volume and the injected concentration of the samples of racemic mixture were carried out simultaneously, using two objective functions. The maximization of the production rate and of the product of the recovery yield and the production rate were performed. Based on the optimum points obtained, the two objective functions were compared for several recovery yield constraints in a range of injected volumes and concentrations. The consequences of choosing a separation design focused on the degree of band overlapping are discussed based on the results of these optimizations.