The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of Bayside's eight exhibition rooms is shown in figure below; the openings between the rooms are numbered 1 to 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 binary integer linear programming model that will enable Bayside's management to determine the locations for the camera systems. If the constant is "1" it must be entered in the box. If your answer is zero, enter "0".

Min	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13
s.t.
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 1
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 2
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 3
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 4
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 5
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 6
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 7
	x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13	- Select your answer -?,?,,=		Room 8

(b)

Solve the model formulated in part (a) to determine how many two-way cameras to purchase.

(?)

Determine where the two-way cameras should be located.

Cameras should be located at openings - Select your answer

-1, 5, 7, 8, 11, and 131,

7, 11, and 122,

4, 9, 11, and 122,

4, 9, and 12

(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 the constant is "1" it must be entered in the box. If your answer is zero, enter "0".

Change the constraint for room 7:

x1+ x2+ x3+ x4+ x5+ x6+ x7+ x8+ x9+ x10+ x11+ x12+ x13

- Select your answer-?,?,,=

(d)

With the policy restriction specified in part (c), determine how many two-way camera systems will need to be purchased.

( ?)

Determine where the two-way camera systems will be located.

Cameras should be located at openings - Select your answer

-1, 2, 6, 7, 11, and 121,

5, 8, 11, and 121,

7, 11, and 123,

6, 9, 12, and 13

(a) Formulate a binary integer linear programming model that will enable Bayside's management to determine the locations for the camera systems. If the constant is "1" it must be entered in the box. If your answer is zero, enter "0". 1 if a camera is located at opening Dif nat Min x1 - x2 + x3 + x4+ x5+ x6 + X7+ x8 + x9 + x10+ x11 + *12 + x13 s.t. x1 + *2 + *3 + x4 + x5+ x6+ x7 + x8+ x9 + x10 + *11 + *12 + x13 - Select your answer - Room 1 1 + *2 + *3 + x4+ x5+ x6+ x7 + x8 + x9 + x10 + x11 + *12 + x13 - Select your answer = Room 2 *1 + x2 + x3 + x4+ x5+ x6 + x7 + x8 + x9 + x10 + x11 + *12 + x13 Select your answer - Room 3 x1 + *2 + x3+ x4+ x5 + x6+ x7 + x8 4 x9 + x10 + x11 + x12 + x13 - Select your answer = Room 4 x1+ x2 + x3 + x4+ x5+ x6 + x7 + x8 + x9 + *10 + x11 + x12 + x13 Select your answer = Room 5 x1 + *2 + x3 + x4+ x5+ *6 + X7+ x84 x9 + x10 + x11 + *12 + x13 Select your answer - Room 6 x1 + x2 + *3 + x4+ x5+ x6 + X7 + X8 + x9 + x10 + x11 + x12 + x13 Select your answer - * Room 7 x1 + x2 + *3 + x4+ x5+ x6 + X7+ x8 x9 + x10 + x11 + *12 + x13 - Select your answer - # Room 8 (b) Solve the model formulated in part (a) to determine how many two-way cameras to purchase. Determine where the two-way cameras should be located. Cameras should be located at openings - Select your answer - (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 the constant is "1" it must be entered in the box. If your answer is zero, enter "0". Change the constraint for room 7: x1 + x2+ x3 + x4 + x5 + x9 + x6 + x7 + x8 + - Select your answer - x10 + x11 + *12 + x13 (d) With the policy restriction specified in part (c), determine how many two-way camera systems will need to be purchased. Determine where the two-way camera systems will be located Cameras should be located at openings - Select your answer -Check My Work (1 remaining) The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of Bayside's eight exhibition rooms is shown in figure below; the openings between the rooms are numbered 1 to 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. 10