Example $6$: Warehouse Layout Problem $($Week $11)$

Consider a warehouse illustrated by the figure below. Nine bays $(6m6m)$ are available for

storage.

Three different types of products $($A$,$ B and C$)$ are to be stored. A type of product cannot share a

bay with any other type of product. The area requirement and weekly load rate for each of these

three products are shown in the table below.

One$-$third $(\frac{1}{3})$ of the shipments has to go through dock $1,$ while the remaining goes through

dock $2.$

Determine the layout that will minimize the average distance travelled per week.