The sexual transmission of HIV/AIDS depends upon the specifics of mixing between subpopulations with differing sexual activity rates. As the manner in which such mixing occurs is very difficult to observe, it is natural to consider the number of infected persons that would result from worst case mixing, that is, mixing that maximizes the number of infected persons in the population. This paper summarizes a recently developed procedure for producing a tight upper bound on the maximum number of infected persons in a population over the long run within the assumptions of a fairly general model of HIV transmission. The technique is illustrated utilizing parameters derived from studies of the AIDS epidemic in San Francisco. An example demonstrating how one might prospectively evaluate an AIDS intervention program using worst case analysis is also discussed.