Dr$.$ Douvas also has estimates of the number of trips made by patients and staff between the various departments each day:

Waiting

Reception

Records$/$

Lounge

Examination

Outpatient Surgery

Reception

$100$

$-$

$-$

$-$

$-$

Records$/$

Lounge

$0$

$150$

$-$

$-$

$-$

Examination

$35$

$5$

$10$

$-$

$-$

Outpatient Surgery

$15$

$5$

$10$

$5$

$-$

Physical Therapy

$50$

$10$

$15$

$40$

$0$

Given that Dr$.$ Douvas wants Reception assigned to area A$,$ how many possible arrangements are there?

Consider the plan shown in the template file. Calculate the total distance traveled for the given solution.

Now select two departments to switch $($except Reception$).$By carefully choosing two, can you come up with a better solution? Justify your answer.