Security System Design. The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of Baysides eight exhibition rooms is shown in the figure on the next page; the openings between the rooms are numbered 1 to 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.

Formulate and solve an integer programming model that will enable Baysides management to determine the locations of the camera systems. Suppose that rooms 1 and 3 have to be served by 2 cameras.

What is the minimum number of cameras required? no decimals.