Dr$.$ Mike Douvas is opening a new sports clinic and is wondering how to arrange the six different departments of the$$ clinic:

A$.$Waiting;

B$.$Reception;

C$.$ Records and staff$$ lounge;

D$.$Examination;

E$.$ Outpatient$$ surgery; and

F$.$ Physical therapy.

The six marked areas are big enough to handle any of the$$ departments, although Dr$.$ Douvas wants to have Reception near the front door$($for obvious$$ reasons$).$ Areas that share a side are approximately $15$ feet$$ apart, while those that share a corner are $25$ feet apart. The distances between A and E and between B and F are $30$feet$,$ while the distances between A and F and between B and E are approximately $45$ feet. Dr$.$ Douvas also has estimates of the number of trips made by patients and staff between the various departments each day.

LOADING... Click the icon to view the map of the clinic.

LOADING... Click the icon to view the number of interdepartmental trips made per day between different departments.

Part $2$

a$.$ If Dr$.$ Douvas wants Reception assigned to area$$ B$,$ the maximum possible number of arrangements is enter your response here. $($Enter your response as a whole$$ number.$)$

Part $3$

b$.$ The total distance of the given layout is enter your response here feet. $($Enter your response as a whole$$ number.$)$