Formulate the min cost flow problem for the following network:

For every node i in N :$=\{$A$,$ B$,...,$ G$\},$ supply$/$demand is given as di in R$.$ Note that i is a

supply node if di $>0($e$.$g$.,$ A$,$ B$),$ a demand node if di $<0($e$.$g$.,$ D$,$ F$,$ G$),$ and a transshipment

node if di $=0($e$.$g$.,$ C$,$ E$).$ For every arc $($i$,$ j$)$ in A :$=\{($A$,$ B$),($A$,$ C$),...,($E$,$ G$)\},$ the unit shipping

cost is given as cij in R$+,$ the capacity $($i$.$e$.,$ upper bound on the amounts of goods flowing on the

arc$)$ is given as uij $,$ and the lower bound lij $=0.$

$4$