Table $2\mathrm{.}1$ shows five customer bases $($node $2$ to $6)$ that are being served by the central warehouse $($node $1).$ Not all customer bases have direct road access to the central warehouse, however, some customer bases are interconnected with roads as shown in Table $2\mathrm{.}1.$ There are $6$ delivery trucks, each is assigned to individual customer bases, setting off from the warehouse.

Question $2$a

Implement an appropriate network model using the information in Table $2\mathrm{.}1$ by drawing the network model. Recommend how should the goods be delivered from the warehouse to each of the customer bases in the most cost$-$efficient way. You are required to show your workings and state any two $(2)$ assumptions to support your approach.

$(20$ marks$)$

Question $2$b

It has been found that the distance provided between customer base $3$ and $6$ is incorrect and is indicated as x on the official map. Verify the range of values for x such that the original solution in Q$2$a remains unchanged.

$(5$ marks$)$