  The minimal grand unified supergravity model is discussed. Requiring
radiative breaking of the electroweak gauge symmetry, the unification of b and
tau Yukawa couplings, a sufficiently stable nucleon, and not too large a relic
density of neutralinos produced in the Big Bang constrains the parameter space
significantly. In particular, the soft breaking parameter m_1/2 has to be less
than about 130 GeV, and the top quark Yukawa coupling has to be near its
(quasi) fixed point. The former condition implies m_gluino < 400 GeV and hence
very large production rates for gluino pairs at the LHC, while the latter
constraint implies that the lighter stop and sbottom eigenstates are
significantly lighter than the other squarks, leading to characteristic
signatures for gluino pair events.
