(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_i 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_i = 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, x₇, x₈, x₉, x₁₀, x₁₁, x₁₂, x₁₃) =

.

(c)

Suppose that management wants to provide additional security coverage for room 7. Specifically, management wants room 7 to be covered by two cameras. Which constraint would have to change?

Room 1Room 2 Room 3Room 4Room 5Room 6Room 7Room 8

What should the new constraint be?

(d)

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

The gallery should install cameras with

(x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, x₉, x₁₀, x₁₁, x₁₂, x₁₃) =

.

entrance to the display rooms. The objective is to provide security coverege for all elght rooms wify the minimum number of tworway cameras