Working memory is a process for the short-term storage and manipulation of information necessary for complex cognitive tasks. During the performance of working memory tasks, the prefrontal cortex (PFC) exhibits sustained persistent activity and is believed to play a key role in the process. Experiments have demonstrated that working memory performance is modulated by dopamine, which is known to be altered in certain pathological conditions, including schizophrenia. A number of models have been proposed for the maintenance of persistent activity in the PFC, often based on either intrinsic cellular bistability or recurrent excitatory connections formed via synaptic adaptation. Consistent with the observation that inhibitory connections dominate the PFC, we present a new approach: a network driven by excitatory-inhibitory interactions where the response to inhibition is modulated by intracellular calcium. Individual neurons fire irregularly, but our model network exhibits emergent properties, such as a clear gamma rhythm. The network is robust to noise and distracters. Only general assumptions about connection probabilities are assumed; the model can represent novel, unlearned stimuli. Dopamine modulates ion channel activity and synaptic conductances. We study the effects of this modulation on cellular and network behavior, and find the experimentally-observed inverted-U shaped relation between dopamine expression and working memory performance.