The Bayside Art Gallery is considering installing a video camera security system to reduce its Insurance premium. A diagram of the eight display rooms that Bayside uses for exhibition is shown in the figure below, the openings between the rooms are numbered through 13. Room 3 Ewe Room 1 Recen 4 Room 7 Room 5 Recom 2 HI + 11 12 Room 6 13 Room A security frm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two roons between which the camera is located. For example, a camera were located at opening sumber 4 rooms 1 and 4 would be covered if a camera were located at opening 11. rooms and would be covered and so on Management decided not to locate a camera system at the entrance to the display room. The objective is to provide security coverage for all light rooms using the minimum number of two-way cameras Cal Formulate 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 a camera is installed at opening and otherwise, for: 1.2.13.3 Min SL Room 1 Room 2 Room 3 Room 4 Room 5 Room 6 Room Room X-0.1. for 1.2.1.13 (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 (X2, X2, X3, X5, X6, *7, *gr *g, *10*111*124*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 O Room 5 Room 6 Room 7 Room 8 What should the new constraint be? () 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 *10*11*124*13)