Consider $10$ patients with locations: $(1,4),(15,8),(9,9),(18,3),(9,15),(2,8),(8,19),(4,14),$

$(14,12),$ and $(15,6).$ There are $4$ potential clinic locations: $(4,4),(9,9),(12,16),$ and $(13,4).$

You are ask to determine the best clinic locations for coverage all patients. The only consideration

is travel distance.

$($a$)$ No patient is willing to travel over $7$ units $($assume travel is according to rectilinear distance$).$

What is the minimum number of clinics that can be opened to serve the population? Where should

they be located?

$($b$)$ Given the same travel condition $(<7$ units$),$ how would you suggest $2$ sites? They can be ones

from the $4$ locations or new locations.

$($c$)$ Consider the equity of traveling to clinics for all patients. How would you determine the clinics

location by minimizing the number of clinics?