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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 Em 1 Room + ++ Hoom 1 HA 12 6 Ener 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; ta camera were located at opening 11, rooms 7 and 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 light 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 (Ley be the 0-1 which is camera is installed at opening and otherwise, for i - 1, 2, -13.) Min Room 1 Room 2 Room) Room 4 Room 5 Room 6 Room Room - 0, 1, fori - 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 (XI. 22, *3. * *31*8*7* *, *9, *10* *21* *121*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 Room 2 Room Room Room 5 Room Room Rooms What should the new constraint be? (d) with the policy restriction specified in part (e), determine how many two-way camera systems will need to be purchased and where they will be locate The gallery should install cameras with , *, *3 ****** *30*23*13*13)