The locus coeruleus (LC) can exhibit tonic or phasic activity and release norepinephrine (NE) throughout the cortex, modulating cellular excitability and synaptic efficacy and thus influencing behavioral performance. We study the effects of LC-NE modulation on decision making in two-alternative forced-choice tasks by changing conductances in a biophysical neural network model, and we investigate how it affects performance measured in terms of reward rate. We find that low tonic NE levels result in unmotivated behavior and high levels in impulsive, inaccurate choices, but that near-optimal performance can occur over a broad middle range. Robustness is greatest when pyramidal cells are less strongly modulated than interneurons, and superior performance can be achieved with phasic NE release, provided only glutamatergic synapses are modulated. We also show that network functions such as sensory information accumulation and short-term memory can be modulated by tonic NE levels, and that previously-observed diverse evoked cell responses may be due to network effects.