Recall the circulation problem which we solved by reducing to max$-$flow problem. We shall now extend this problem further. There is a flow network G $=($V$,$E$)$with source s$,$sink t in V and nonnegative edge capacities $\{$ce$\}.$Each vertex v has a demand dv which is a real number. In addition each edge has a nonnegative number le$.$Design a polynomial time algorithm to determine if there exists a circulation f : E $$R such that $($a$)$For each vertex v$,$fin$($v$)$fout$($v$)=$dv$.($b$)$For each edge e$,$le $$f$($e$)$ce$.$Hint: Reduce this problem to an instance of circulation problem without any lower bound on edges.