Problem 7-21 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 1-13. 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 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. Use a software package LINGO. Room 3 2 Entrance Room 1 4 Room 4 S Room 7 8 Room 9 Room 2 10 11 12 Room 6 13 Room 8 a. Formulate a 0-1 integer linear programming model that will enable Bayside's management to determine the locations for the camera systems. If constant is "1", it must be entered in the box. Let X; = 1 if a camera is located at opening i, o if not. Min X1 + X2 + X3 + X4 + X + X6 + X7 + X8 + X9 + X10 + X11 + X12 + X13 X1 + X4 + Room 1 X6 + X9 + X12 Room 2 X1 + X2 + X3 Room 3 X3 + X4 + X5 + X7 Room 4 X7 + x8+ X9 + X10 Room 5 X10 + X12 + X13 Room 6 X2 + X5 + X9 + X11 Room 7 X11 + X13 Room 8 Xi = 0,1 i = 1, 2, ..., 13 b. Solve the model formulated in part (a) to determine how many two-way cameras to purchase. Solve the model formulated in part (a) to determine where the two-way cameras should be located. The input in the box below will not be graded, but may be reviewed and considered by your instructor. c. Suppose that management wants to provide additional security coverage for room 7. Specifically, management wants room 7 to be covered by two cameras. How would your model formulated in part (a) have to change to accommodate this policy restriction? If constant is "1", it must be entered in the box. Change the constraint for room 7 to X2 + X5 + X9 + X11 d. With the policy restriction specified in part (c), determine how many two-way camera systems will need to be purchased. With the policy restriction specified in part (c), determine where the two-way camera systems will be located. The input in the box below will not be graded, but may be reviewed and considered by your instructor