The Bayside Art Gallery Is Considering Installing A Video Camera Security System To Reduce Its Insurance Premiums A Dia 1 (45.39 KiB) Viewed 13 times
The Bayside Art Gallery Is Considering Installing A Video Camera Security System To Reduce Its Insurance Premiums A Dia 2 (32.84 KiB) Viewed 13 times
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. Entrance Room 1 Room 2 Room 12 Room + F 10 Room 5 Room 6 1 Room 7 + 13 Room 8 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 x, be the 0-1 which is 1 if a camera is installed at opening, and 0 otherwise, for 1, 2, 13.) Min st... 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 (X₂ X₂ cameras with X X10 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 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
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