Problem $3.$

Suppose we need to locate a new factory in relation to five other existing facilities with the coordinates $($in kilo meters$-$km$)$ as follows: Raw Material Storage $(20,30)$; Finished Products Storage $(40,60)$; Distribution Warehouse $1(80,50)$; Distribution Warehouse $2(100,40)$; Assembly Factory $(50,30).$ Total material flow to these five current existing facilities is $50,6020,40$ and $80$ tons per month and the transport costs are $2$ $$/$ton$-$km$.$ Find the optimal location for the new factory using the minisum rectilinear distance.