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4 I-20 Points DETAILS ASWMSC115 7.E.021. MY NOTES ASK YOUR TEACHER The Bayside Art Gallery in considering installing a video camera security system to reduce its insurance precniunt. A diagram of the right doplay rooms that Beyside uses for exhibition is shown in the figure below, the openings between the rooms are numbered 1 through 13. Room 3 2 En Room . Room 4 S Room 7 Rice 5 Room 2 10 ti H + Roces Room 2 10 11 12 Rece 6 13 Room A security firm proposed that two-way cameras be installed at some room openings. Each camera has the by to monitor the two rooms between which the camera s 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 1 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 a camera is installed at opening, and otherwise, for I - 1,2,...13.) Min st Room 1 Room 2 Room Room 4 Room 5 Room 6 Room? Room a 12 (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 y, X 11. zu (c) Suppose that management wants to provide additional security coverage for room 7. Specifically, management wants room 7 to be covered by two cameranWhich constraint would have to change? Room 1 Room 2 Room 3 Room 4 Rooms Room 6 Room 7 Room What should the new constraint be? (a) with the policy restriction specified in part ( determine how many two way camera systems will need to be purchased and where they will be located The gallery should install camera with Y