Four hospitals located within a city are cooperating to establish a centralized blood$-$

bank facility that will serve the hospitals. The new facility is to be located such that

the $($total$)$ distance traveled is minimized. The hospitals are located at the following

coordinates: P$1=(5,10),$ P$2=(7,6),$ P$3=(4,2),$ and P$4=(16,3).$ The number of deliveries

to be made per week between the blood$-$bank facility and each hospital is estimated

to be $3,8,2,$ and $10,$ respectively.

$1.$ Assuming Manhattan distance, formulate a linear programming model and

determine the optimal location