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 figure below; the openings between the rooms are numbered 1 through 13. Room 2 Entrance Room 3 Room 4 5 Room 7 8 Room 5 9 Room 2 10 12 Room 6 13 Room 8 1 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 0-1 integer linear programming model that will enable Bayside's management to determine the locations for the camera systems. (Let xbe the 0-1 which is 1 if a camera is installed at opening i, and otherwise, for i = 1, 2, ... 13.) Min s.t. Room 1 Room 2 Room 3 Room 4 Room 5 Room 6 Room 7 Room 8 x;= 0, 1, for i = 1, 2, ... 13 (b) Solve the model formulated in part (a) to determine how many two-way cameras to purchase and where they should be located. The gallery should install cameras with (X14 X2, X3, X4, X5, X6 X7*g. 9, *10*11' *12*13) = (c) Suppose that management wants to provide additional security coverage for room 7. Specifically, management wants room 7 to be covered by two cameras. Which constraint would have to change? Room 1 Room 2 Room 3 Room 4 Room 5 O Room 6 Room 7 Room 8 What should the new constraint be? (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. The gallery should install cameras with (x1, x2, 3, 4, 5, 6, 7, xg, xg, *10*11* *12: *13) =