Exercise $7\mathrm{.}10$ Consider the uncapacitated network flow problem shown in Figure $7\mathrm{.}38.$ The label next to each arc is its cost. Consider the spanning tree indicated by the dashed arcs in the figure and the associated basic solution.

$($a$)$ What are the values of the arc flows corresponding to this basic solution? Is this a basic feasible solution?

$($b$)$ For this basic solution, find the reduced cost of each arc in the network.

$($c$)$ Is this basic solution optimal?

$($d$)$ Does there exist a nondegenerate optimal basic feasible solution?

$($e$)$ Find an optimal dual solution.

$($f$)$ By how much can we increase $\backslash ($ c$\_\{56\}\backslash )[$the cost of arc $\backslash (\backslash$left$.(5,6)\backslash$right$]\backslash )$ and still have the same optimal basic feasible solution?

$($g$)$ If we increase the supply at node $1$ and the demand at node $9$ by a small positive amount $\backslash (\backslash$delta $\backslash ),$ what is the change in the value of the optimal cost?

$($h$)$ Does this problem have a special structure that makes it simpler than the general uncapacitated network flow problem?

I need the solution for all parts of this linear programming question.