Question $5(25$ marks$)$

A practical cxample of minimum cost flow is shown in Figure Q$5$ below. The goal is to identify the maximised flow among sources and demand nodes at the lowest total cost. Node G and Node H are destinations $($or Demand$)$ nodes, requiring $30$ and $70$ units, respectively, whereas Node A is an origin $($or Source$)$ node supplying $100$ units.

$($a$)$ Regardless of the demand requirement $(30$ and $70),$ describe the flow from the Source $($Node A$)$ to Demand $($Node G and Node H$)$ that will attain maximum flow.

$(7$ marks$)$

$($b$)$ With the specific demand requirement given in Node G and Node H$,$ calculate the minimum cost flow in a Stepwise manner.

$(8$ marks$)$

$($c$)$ Is there any other scenario$($s$)$ other than logistics and transportation, where the minimum cost maximum flow problem is applicable? If your answer is Yes, provide TWO examples.

$(4$ marks$)$

$($d$)$ Consider a scenario where the cost or capacity of an edge in the network changes over time. How would these changes affect the minimum cost flow? What strategies could be used to handle such dynamic changes?

$(6$ marks$)$

Figure Q$5-$Cost Flow from Node A to Node H