Consider four departments $-$ A$,$ B$,$ C$,$ and D $-$ in adjacent offices on one side of the hall. Department $A$ is at one end of the hall, located next to B$.$ Department B is between departments A and C$,$ and department D is at the other end of the hall. Each day, workers from department A make ten trips each to departments B$,$ C$,$ and D$.$ Workers from department B make twenty trips each day to the other departments, workers from $C$ make thirty trips daily to each of the other departments, and workers from $D$ make forty trips to e$$ch other department. Which of these exchanges would result in an improved layout from the perspective of minimizing the distance traveled?

a$.$ Exchanging the offices of $D$ and $A$

b$.$ Exchanging the offices of $C$ and $D$

c$.$ Exchanging the offices of A and $B$

d$.$ Exchanging the offices of $B$ and $C$