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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 i, and 0 otherwise, for i = 1, 2, ..., 13.) Min s.t. 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 cameras with (X1, X2 X3 X4 X5 X6 X, X, X, X10' x 11' X 12'x13): 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 3 Room Room 4 4 7 7 Room 8 5 10 11 12 Room 13 Room 6 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 i, and 0 otherwise, for i = 1, 2, ..., 13.) Min s.t. 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 cameras with (X1, X2 X3 X4 X5 X6 X, X, X, X10' x 11' X 12'x13): 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 3 Room Room 4 4 7 7 Room 8 5 10 11 12 Room 13 Room 6 8

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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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 i, and 0 otherwise, for i = 1, 2, ..., 13.) Min s.t. 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 cameras with (X1, X2 X3 X4 X5 X6 X, X, X, X10' x 11' X 12'x13):
Transcribed Image Text: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 i, and 0 otherwise, for i = 1, 2, ..., 13.) Min s.t. 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 cameras with (X1, X2 X3 X4 X5 X6 X, X, X, X10' x 11' X 12'x13):
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 3 Room Room 4 4 7 7 Room 8 5 10 11 12 Room 13 Room 6 8
Transcribed Image Text: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 3 Room Room 4 4 7 7 Room 8 5 10 11 12 Room 13 Room 6 8
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