  We investigate the optimal tradeoff between sensitivity and field of view in
surveys for slow radio transients using the event detection rate as the survey
metric. We investigate (i) a survey in which the events are distributed
homogeneously throughout a volume centred on the Earth, (ii) a survey in which
the events are homogeneously distributed, but are only detectable beyond a
certain minimum distance, and (iii) a survey in which all the events occur at
an identical distance, as is appropriate for a targetted survey of a particular
field which subtends N_point telescope pointings. For a survey of fixed
duration, T_obs, we determine the optimal tradeoff between number of telescope
pointings, N, and integration time per field. We consider a population in which
the event luminosity distribution follows a power law with index -\alpha, and
t_slew is the slewing time between fields or, for a drift scan, the time taken
for the telescope drift by one beamwidth. Several orders of magnitude
improvement in detection rate is possible by optimization of the survey
parameters. The optimal value of N for case (i) is N_max ~ T_obs/4 t_slew,
while for case (iii) we find N_max = (L_max/L_0)^2 [ (3 -\alpha)/2
]^{2/(\alpha-1)}, where L_max is the maximum luminosity of a transient event
and L_0 is the minimum luminosity event detectable in an integration of
duration T_obs. For a telescope field of view, \Omega, and a minimum detectable
flux density, S_0, the detection rate scales as N \Omega S_0^{-3/2} for
homogeneously distributed events, while for targetted events (iii) it scales as
N \Omega S_0^{1-\alpha}. The quantity \Omega S_0^{-2} is often used as the
metric of telescope performance in the SKA transients literature, but only
under special circumstances is it the metric that optimizes the event detection
rate. [abstract abbreviated]
