A new hospital and a fire station will be built to serve a large neighborhood consisting of just$-$established housing estates. The distance between the two new facilities is not under consideration. Transportation from some of the residential sites $($group R$)$ to the new facilities can be calculated according to perpendicular and parallel roads. However, since the construction of all roads in the neighborhood has not been completed, the transportation distances from the others $($group E$)$ to the new facilities are calculated according to the possible straight lines. The locations of the residential sites and the number of residents in each one are given in Table $1.$ Figure $1$ also shows the boundaries of the area where roads are being built and therefore where new facilities can be located. $($The new hospital and the fire station must be within area R$.)$

According to the given data and information, determine optimal $($or near$-$optimal$)$ locations for both the new hospital and fire station. $($To use rectilinear and Euclidean distances together, develop your own approach.$)$

Then, calculate the distance$-$based objective function value for two new facilities.

Table $1$: Data about residential sites

$\backslash$table$[[$Res$.$ Site,Group,Coordinates,# of Residents$],[1,R,(1,9),800],[2,R,(2,3),700],[3,R,(6,11),400],[4,R,(10,5),750],[5,R,(11,16),1000],[6,R,(14,3),1200],[7,R,(17,8),650],[8,R,(19,19),500],[9,E,(2,13),300],[10,E,(4,19),250],[11,E,(7,15),700],[12,E,(9,17),800]]$

Figure $1$: Representation of the whole neighborhood