We compute the Bieri-Neumann-Strebel invariants (Formula presented.) for the generalized solvable Baumslag-Solitar groups (Formula presented.) and their finite index subgroups. Using (Formula presented.), we show that certain finite index subgroups of (Formula presented.) cannot be isomorphic to (Formula presented.) for any k. In addition, we use the BNS-invariants to give a new proof of property (Formula presented.) for the groups (Formula presented.) and their finite index subgroups.