The file P06_92.xlsx lists the distances between 21 U.S. cities. We want to locate liver transplant centers in a subset of these 21 cities.

a. Suppose we plan to build four liver transplant centers and our goal is to minimize the maximum distance a person in any of these cities has to travel to a center. In which cities should the centers be located?

b. How many centers are needed, and in which cities should they be located, so that residents of all cities are within 800 miles of a transplant center? (The model must be linear.)

c. We know that a transplant center is sometimes filled to capacity. With this in mind, we would like everyone to be relatively close to two transplant centers. How many centers are needed, and in which cities should the centers be located, to ensure that residents of all cities are within 800 miles of two transplant centers? (Again, the model must be linear.)

d. The file P06_92.xlsx also lists the number of people

(in millions) living in each city’s metropolitan area.

Where should we locate three transplant centers to maximize the number of people within 800 miles of a transplant center?