Task $4(20$ marks$)$

The National Express Parcel Service has established various truck and air routes over which it ships

parcels. The holiday season is approaching, which means a dramatic increase in the number of

packages that will be sent. The service wants to know the maximum flow of packages it can

accommodate $($in tons$)$ from station $1$ to station $7.$ The network of routes and the flow capacities $($in

tons of packages per day$)$ along each route are shown in the network below:

Determine the maximum tonnage of packages that can be transported per day from station $1$ to

station $7$ and indicate the flow along each branch. $[$You need to show step by step workings$]$