Copyright 2007 ICST. We present a case study of business and systems modelling for a Utility Computing service. Our analysis is concerned mainly with service pricing, resource flexing, and costs related to preventive security measures. We explain the conceptual and mathematical basis of our modelling approach, describing the details of a particular (discrete event, executable) model of a Utility Computing service, and show how the information obtained from such a model can aid business and design decisions.