  We consider the Yamabe invariant of a compact orbifold with finitely many
singular points. We prove a fundamental inequality for the estimate of the
invariant from above, which also includes a criterion for the non-positivity of
it. Moreover, we give a sufficient condition for the equality in the
inequality. In order to prove it, we also solve the orbifold Yamabe problem
under a certain condition. We use these results to give some exact computations
of the Yamabe invariant of compact orbifolds.
