Question: The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in the following figure; the openings between the rooms are numbered 1-13. A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be covered; and so on. Management decided not to locate a camera system at the entrance to the display rooms. The objective is to provide security coverage for all eight rooms using the minimum number of two-way cameras.
a. Formulate a binary integer linear programming model that will enable Bayside's management to determine the locations for the camera systems.
b. Solve the model formulated in part a to determine how many two-way cameras to purchase and where they should be located.
c. Suppose that management wants to provide additional security coverage for room 7. Specifically, management wants room 7 to be covered by two cameras. How would the model you formulated in part a have to change to accommodate this policy restriction?
d. With the policy restriction specified in part c, determine how many two-way camera systems will need to be purchased and where they will be located.
