$[$Question $4](15\%$ of total marks$)$

Tesco has recently opened a new depot located in Birmingham. They are currently planning a

transportation network that aims to deliver goods from the depot to seven other Tesco Superstores

and Tesco Extra shops $($labelled as $1,2,3,4,56,$ and $7)$ in West Midlands. The monthly average

amount of goods to be delivered from the depot to each shop is estimated as $12,12,6,16,15,10,$

and $8$ tonnes, respectively. The distance between shops and depot $($labelled as D$)$ is presented in

terms of miles in the following table.

D $1234567$

D $--4424524$

$14--568843$

$245--25867$

$3262--2547$

$44852--347$

$558853--47$

$6246444--3$

$74377773--$

The management team would like to operate with the minimum number of trucks in their fleet and

to specify the routes of trucks to deliver goods from the depot to each store. They assume that each

truck has a capacity of $30$ tonnes of goods to carry.

Apply the savings algorithm to determine the number of trucks and their routes.