QUESTION $3(40$ points$)$

Get$-$Warm Hospital is a new small emergency process$-$oriented facility to be located in a popular ski resort in Ellicottville. Its new administrator, Mary, decides to organize the hospital using the process$-$layout method she studied in business school.

The layout of the facility is given below. The distance between each adjacent area is $40$ft$.$ For example the distance between A and $E$ is $40ft,$ the distance between A and $B$ is $40ft,$ and the distance between A and $H$ is $160ft.$

$\backslash$table$[[$Area A$,$Area B$,$Area C$,$Area D$],[$Area E$,$Area F$,$Area G$,$Area H$],[,,,]]$

There are eight departments to be located in these eight areas namely, Entrance, Exam room $1,$ Exam room $2,$ X$-$ray, Lab Test and EKG, Operating room, Recovery room, and Cast$-$setting room. The flows between the departments are given in the following matrix.

$\backslash$table$[[,$Average Number of Patient Flows per Day,,$],[,$ENT,EX$1,$EX$2,$XR$,$Lab,OR$,$RR$,$CS$,],[$Entrance $($ENT$),,,25,60,75,10,20,10,20],[$Exam Room $1($EX$1),,,50,30,40,35,10,45,],[$Exam Room $2($EX$2),,,,,25,65,20,30,35],[$X$-$ray $($XR$),,,,,,95,12,25,],[$Lab test$/$EKG $($Lab$),,,,,,,90,10,],[$Operation Room $($OR$),,,,,,,,15,],[$Recovery Room $($RR$),,,,,,,,20,],[$Cast$-$setting Room $($CS$),,,,,,,,,]]$

Find the best assignment of the departments to the areas that minimizes the total distance travelled.