  We obtain lower and upper bounds for the maximum weight of a directed cut in
the classes of weighted digraphs and weighted acyclic digraphs as well as in
some of their subclasses. We compare our results with those obtained for the
maximum size of a directed cut in unweighted digraphs. In particular, we show
that a lower bound obtained by Alon, Bollobas, Gyafas, Lehel and Scott (J Graph
Th 55(1) (2007)) for unweighted acyclic digraphs can be extended to weighted
digraphs with the maximum length of a cycle being bounded by a constant and the
weight of every arc being at least one. We state a number of open problems.
