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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 figure below; the openings between the rooms are numbered 1-13. 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.
A) Formulate a 0-1 integer linear programming model that will enable Baysides management to determine the locations for the camera systems. (in excel and I have to solve using the solver)
B) Solve the model formulated in part (a) to determine how many two-way cameras to purchase and where they should have been located.
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