Question $3$:

Consider the network in the figure below. In this network, the values on the links represent the lengths of the links, and the nodes $\{A,B,C,D\}$ in the network indicate the customers.

The decision maker would like to establish a distribution center in this network so that the maximum distance to each customer is minimized.

a$)$ What is the optimal solution when the distribution center is located at one of the nodes?

b$)$ What is the optimal solution when the distribution center is allowed to be located at nodes and links?

c$)$ What is the optimal solution when the distribution center is allowed to be located at all nodes and only at links $A,D$ or $C,D?$

$($Please clearly state the optimal location of the distribution center and the optimal objective function value for the solution in each option$).$