In this problem we will design a surveillance system. Suppose we have 10 locations that we would like to monitor, and 5 potential cameras that we can install:
Camera 1 can view locations 1,2,3,4,10 Camera 2 can view locations 3,4,5,6 Camera 3 can view locations 5,6,7 Camera 4 can view locations 7,8,9 Camera 5 can view locations 1,2,8,9,10
A. Formulate an integer linear program that minimizes the number of cameras installed, such that each location can be viewed by at least one camera. Clearly define your decision variables, objective function, and constraints.
B. Now suppose that different cameras cost different amounts of money. Let camera i cost c dollars, for i= 1,2,3,4,5. Formulate a ILP that maximizes the number of locations viewed, subject to the constraint that the total cost of all cameras purchased is at most B dollars.