For the network of Figure 4.2, show that only one facility is needed to cover all demands if the coverage distance is 19 or more. At what two nodes can the facility be located? (a) For the network...

For the network of Figure 4.2, show that only one facility is needed to cover all demands if the coverage distance is 19 or more. At what two nodes can the facility be located?

(a) For the network shown in Figure 4.24, write down the objective function and constraints for a set covering problem (with facilities located only on the nodes) using a coverage distance of 10.

(b) Solve the set covering problem that you formulated. Clearly indicate which locations are dominated by which other locations. Also, clearly indicate how many facilities are needed and where they should be located.