  By fitting a flexible stellar anisotropy model to the observed surface
brightness and line-of-sight velocity dispersion profiles of Draco we derive a
sequence of cosmologically plausible two-component (stars + dark matter) models
for this galaxy. The models are consistent with all the available observations
and can have either cuspy Navarro-Frenk-White or flat-cored dark matter density
profiles. The dark matter halos either formed relatively recently (at z~2...7)
and are massive (up to ~5x10^9 M_Sun), or formed before the end of the
reionization of the universe (z~7...11) and are less massive (down to ~7x10^7
M_Sun). Our results thus support either of the two popular solutions of the
"missing satellites" problem of Lambda cold dark matter cosmology - that dwarf
spheroidals are either very massive, or very old. We carry out high-resolution
simulations of the tidal evolution of our two-component Draco models in the
potential of the Milky Way. The results of our simulations suggest that the
observable properties of Draco have not been appreciably affected by the
Galactic tides after 10 Gyr of evolution. We rule out Draco being a "tidal
dwarf" - a tidally disrupted dwarf galaxy. Almost radial Draco orbits (with the
pericentric distance <15 kpc) are also ruled out by our analysis. The case of a
harmonic dark matter core can be consistent with observations only for a very
limited choice of Draco orbits (with the apocentric-to-pericentric distances
ratio of <2.5).
