Utility plants are widely used to meet cooling, heating, and, in many cases, electricity needs of large manufacturing plants and commercial facilities. Efforts to increase energy efficiency and reduce environmental footprint of these facilities have gained significant traction in recent years. In this paper, we present an optimization problem derived by employing accurate models for each process unit and simulation studies that underscore some key challenges in optimal operation of utility plants. We also demonstrate the value of a model-based approach to systematic optimization of the utility plant operation. We show that even for relatively simple systems the decision for optimal operation is nonintuitive.