You need to build a hospital to serve six communities A to F. Data about each community and a noisy factory in the area are given in the following table Community Population (thousands) X (miles) Y (miles) A 10 30 50 B 40 20 70 C 30 25 60 D 20 35 90 E 40 70 120 F 35 90 40 Noisy factory 35 50 Find the best location for the hospital that: a. Minimizes the total distance traveled by all the residents to the hospital. b. Minimizes the maximum distance to the hospital for all customers. You wish to build the hospital at least 30 miles from the noisy factory. Find the best location for the hospital that: c. Minimizes the total distance traveled by all the residents to the hospital. d. Minimizes the maximum distance to the hospital for all customers.