A new library is needed on the campus $.$ After extensive research,

the university board has narrowed down its choice to two possible sites.

The locations for the current faculties, expected students from each

faculty, and possible locations for the library are shown in the tables

below.

a$.$ Determine the optimal location for the new library such that the

total distance the students have to travel is minimized. It is fair

to assume that the construction cost for all three sites is similar

and distance is measured rectilinearly.

b$.$ Determine the minimax distance $($considering weights, and then

ignoring weights$).$