Globular Cluster Abundances from High-Resolution, Integrated-Light
  Spectroscopy. III. The Large Magellanic Cloud: Fe and Ages
  In this paper we refine our method for the abundance analysis of high
resolution spectroscopy of the integrated light of unresolved globular clusters
(GCs). This method was previously demonstrated for the analysis of old ($>$10
Gyr) Milky Way GCs. Here we extend the technique to young clusters using a
training set of 9 GCs in the Large Magellanic Cloud (LMC). Depending on the
signal-to-noise ratio of the data, we use 20-100 Fe lines per cluster to
successfully constrain the ages of old clusters to within a $\sim$5 Gyr range,
the ages of $\sim$2 Gyr clusters to a 1-2 Gyr range, and the ages of the
youngest clusters (0.05-1 Gyr) to a $\sim$200 Myr range. We also demonstrate
that we can measure [Fe/H] in clusters with any age less than 12 Gyrs with
similar or only slightly larger uncertainties (0.1-0.25 dex) than those
obtained for old Milky Way GCs (0.1 dex); the slightly larger uncertainties are
due to the rapid evolution in stellar populations at these ages. In this paper,
we present only Fe abundances and ages. In the next paper in this series, we
present our complete analysis of the $\sim 20$ elements for which we are able
to measure abundances. For several of the clusters in this sample, there are no
high resolution abundances in the literature from individual member stars; our
results are the first detailed chemical abundances available. The spectra used
in this paper were obtained at Las Campanas with the echelle on the du Pont
Telescope and with the MIKE spectrograph on the Magellan Clay Telescope.
