The ``steady-state'' condition 
in Equation (1)
can be rewritten as
Consider 
(see
Equation (1)).
The minimum of 
is obtained for 
. The expression of shows that is a non-increasing function of
P when 
, and then a non-decreasing function of
P when 
. Also, note that 
does not depend on
P (except than through the condition 
). Then
the result follows according to a simple case
analysis.
For large domains, we will have 
,
and it is no surprise that the optimal number of processors is the one required
to ensure steady-state execution.