A manufacturer wants to construct warehouses in six different locations of the city to supply dry cells to his customers on time. The manufacturer wants to construct the minimum number of warehouses such that each warehouse is within 40 miles of at least one other warehouse. The following table provides the distance (in miles) between the locations.

A manufacturer wants to construct warehouses in six different locations of the city to supply dry cells to his customers on time. The manufacturer wants to construct the minimum number of warehouses such that each warehouse is within 40 miles of at least one other warehouse. The following table provides the distance (in miles) between the locations.

From Location ALocation BLocation CLocation DLocation ELocation F

Location A 0 35 40 45 60 70

Location B 0 35 40 70 75

Location C 0 45 50 50

Location D 0 40 50

Location E 0 30

Location F 0

(1) Formulate and solve an integer linear program that can be used to determine the minimum number of warehouses needed to be constructed. What are their locations?

(2) Solve the IP in (1) by running Solver. Be sure to copy and paste the Answer report at the appropriate place in your homework submission. What are the optimal solution and the optimal objective function value?

(1) Formulate and solve an integer linear program that can be used to determine the minimum number of warehouses needed to be constructed. What are their locations?

(2) Solve the IP in (1) by running Solver. Be sure to copy and paste the Answer report at the appropriate place in your homework submission. What are the optimal solution and the optimal objective function value?