1. [-/25 Points] DETAILS MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Grave City is considering the relocation of several police substations to obtain better enforcement in high-crime areas. The locations under consideration together with the areas that can be covered from these locations are given in the following table. Potential Locations for Substations Areas Covered 1, 5, 7 M 4, 5, 6 1, 3, 5 1, 2, 5, 7 1, 5, 6, 7 Q 2, 4, 5 R 3,4,6 (a) Formulate an integer programming model that could be used to find the minimum number of locations necessary to provide coverage to all areas. (Letx, = { 1 if a substation is located at area i for i = L, M, N, O, P, Q, O otherwise P, Q, R.) Min s.t. Area 1 Area 2 Area 3 Area 4 Area 5 Area 6 Area 7 (b) Solve the problem in part (a). What locations should be given substations? (Select all that apply.) Location L Location M O Location N O Location O Location P Location Q O Location R (c) Using equation (13.1), (Sum of variables in the set o) - (sum of variables in the set z) = (number of variables in the set o) - 1 where O is the set of binary variables in our original optimal solution set to one and Z is the set of those set to zero, find a second-best solution. What is the increase in cost (in $) versus the best solution from part (b)? Need Help? Read It