Ford$-$Fulkerson theorem$)$ in the textbook in section $9\mathrm{.}3,$

Consider the following digraph:

$($a$)$ Find a maximum flow from source $($node r$)$ to sink

$($node s$)$ in the digraph, using the Ford$-$Fulkerson algorithm. Describe

Each step clearly.

$($b$)$ Describe the problem as an LP problem.

$($c$)$ Werify the truth of the Max$-$Flow$/$Min$-$Cut Theorem for the network

Flow which you found in $($a$).$ Start by finding all the feasible

$(r,s)-$cuts. What would be the maximum flow if the direction of

The arrow from a to cwere reversed? $($Use the Max$-$Flow Min$-$Cut

Theorem to determine this.$)$