Purdue Clinic at Waldron Street was established in 1966 as West Lafayette's community health care center. The center decided to initiate its "Intoxication Treatment Program" due to recent public demand and increased budget from the city council.

Intoxication treatment includes administration of IV fluids and B complex vitamins for dehydration and vitamin deficiency that can cause serious brain injuries. In severe cases the patient will be intubated to support respiration and to protect the lungs from filling with vomit.

The center's manager was recommended to allocate a facility room for the new program. The manager identified five rooms that would have high travel frequency to the facility room of the new program. The coordinates of these rooms and their expected travel frequency to the new facility room per day are as follows.

X Y Expected travel frequency per day
Main office 40 30 25
Nurses room 50 45 35
Doctor room 40 45 30
Supplies room 30 25 12
File room 60 35 15

Determine the location of the room with rectilinear distance that

a.) Minimize the maximum travel distance per trip, please draw the graph and demonstrate how you find the optimal solution.
b.) Use the formula to solve this problem, and check the solution with the result of problem (a).