The 2009 A (H1N1) influenza pandemic was rather atypical. It began in North America at the start of the spring and in the following months, as it moved south, efforts to develop a vaccine that would mitigate the potential impact of a second wave were accelerated. The world's limited capacity to produce an adequate vaccine supply over just a few months resulted in the development of public health policies that "had" to optimize the utilization of limited vaccine supplies. Furthermore, even after the vaccine was in production, extensive delays in vaccine distribution were experienced for various reasons. In this note, we use optimal control theory to explore the impact of some of the constraints faced by most nations in implementing a public health policy that tried to meet the challenges that come from having access only to a limited vaccine supply that is never 100% effective.