One of the simplest measures of the success of an optimization system is its ability to correctly identify the optimum process operations policy. In the case of a model-based real-time optimization system, few tools are available to the system designer for investigating the suitability of a candidate process mode for use in such systems. This paper presents point-wise model adequacy checking methods, both analytical and numerical, for determining the ability of the model-based optimization system to have an optimum coincident with that of the true process. The paper concludes with a case study using the reactor for the Williams-Otto plant, where two different approximations to the reaction sequence are tested for point-wise model adequacy.