(a) Use the SITATION program to find the solution of the vertex 10-center problem on the 88-node problem (CITY1990.GRT). Find the minimum coverage distance such that all demands can be covered by 10...

(a) Use the SITATION program to find the solution of the vertex 10-center problem on the 88-node problem (CITY1990.GRT). Find the minimum coverage distance such that all demands can be covered by 10 facilities accurate to 1 mile. Use a binary search over an appropriate interval such as 340–400 miles. Clearly show your results.

Important note: To solve this exercise, use the Lagrangian relaxation upper bounds. Set the Lagrangian parameters as follows:

(b) Repeat part (a), but now find the 8-center solution.

(c) Repeat part (a), but now find the 9-center solution.

(d) What do the solutions to parts (b) and (c) imply about the marginal value of the additional facility in terms of the P-center objective as you go from eight to nine facilities?

(e) What do the solutions to parts (a) and (c) imply about the marginal value of the additional facility in terms of the P-center objective as you go from 9 to 10 facilities?