$[$Question $2](24\%$ of total marks$)$

World Beer Supply $($WBS$)$ is a speciality beer supplier delivering $123$ different brands of beer to

$20,000$ customers all over the UK$,$ grouped into $89$ regions. They have two central warehouses, and

five regional distribution centres. Customers are either served from a regional distribution centre, or

directly from the central warehouse. The regional distribution centres have their inventory

replenished from the central warehouse twice a week. Due to increased demand, WBS plans to build

a sixth regional distribution centre. Five different possible locations have been identified.

You may assume that you have access to all the necessary data, including

$-$ The expected demand in each region Di

$-$ The transportation cost per unit of demand from each warehouse$/$distribution centre to

each region cij

$-$ The capacity of each warehouse$/$distribution centre Kj

$-$ The fixed operating cost for each warehouse$/$distribution centre Fj$.$