The bayside art gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the
The Bayside Art Gallery is considering the installation of a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms used by the gallery is shown in the figure on the right; the openings between the rooms are numbered from 1 to 13. A security firm has proposed that two-way cameras be installed at some of these room openings. Each camera can monitor the two rooms between which it is positioned. For example, if a camera is installed at opening number 4, it will cover rooms 1 and 4; if the camera is located at opening number 11, it will cover rooms 7 and 8, and so on. Management has decided not to install a camera system at the entrance to the rooms. The objective is to ensure security coverage for all eight rooms using the minimum number of two-way cameras.
a. Develop a mathematical binary integer linear programming model that will assist the management of the art gallery in determining the optimal locations for the camera system. Be sure to state your decision variables, objective function, and constraints.
b. Solve the model you formulated in part a using Excel Solver to determine how many two-way cameras need to be purchased and where they should be located.
c. Suppose that management wants to provide additional security coverage specifically for room 7. The requirement is for room 7 to have coverage from two cameras. How would your model from part a need to be modified to accommodate this policy restriction? (Hint: specify the changed constraint.)
d. With the policy restriction outlined in part c, determine how many two-way camera systems need to be purchased and identify their optimal locations.
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