  We explore the relationship between young, embedded binaries and their parent
cores, using observations within the Perseus Molecular Cloud. We combine
recently published VLA observations of young stars with core properties
obtained from SCUBA-2 observations at 850 um. Most embedded binary systems are
found toward the centres of their parent cores, although several systems have
components closer to the core edge. Wide binaries, defined as those systems
with physical separations greater than 500 au, show a tendency to be aligned
with the long axes of their parent cores, whereas tight binaries show no
preferred orientation. We test a number of simple, evolutionary models to
account for the observed populations of Class 0 and I sources, both single and
binary. In the model that best explains the observations, all stars form
initially as wide binaries. These binaries either break up into separate stars
or else shrink into tighter orbits. Under the assumption that both stars remain
embedded following binary breakup, we find a total star formation rate of 168
Myr^-1. Alternatively, one star may be ejected from the dense core due to
binary breakup. This latter assumption results in a star formation rate of 247
Myr^-1. Both production rates are in satisfactory agreement with current
estimates from other studies of Perseus. Future observations should be able to
distinguish between these two possibilities. If our model continues to provide
a good fit to other star-forming regions, then the mass fraction of dense cores
that becomes stars is double what is currently believed.
