question $4$ hw$7$

below; the openings between the rooms are numbered $1$ through $13.$

$($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 instal

cameras with $(x_{1^{\text{'}}}{x}_{2^{\text{'}}}{x}_{3^{\text{'}}}{x}_{4^{\text{'}}}{x}_{5^{\text{'}}},x_{6^{\text{'}}},x_{7^{\text{'}}},x_{8^{\text{'}}},x_{9^{\text{'}}}{x}_{{10}^{\text{'}}}{x}_{{11}^{\text{'}}},x_{{12}^{\text{'}}}{x}_{13})=(|).$

$($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 $2$

Room $3$

Room $4$

Room $5$

Room $6$

Room $7$

Room $8$

What should the new constraint be$?$

$($d$)$ With the policy restriction specifed in part $($c$),$ determine how many twoway camera systems will need to be purchased and where they will be located.

The gallery should install

entrance to the display rooms. The objective is to provide security coverage for all eight rooms using the minimum number of two$-$way cameras.

opening $i,$ and $0$ otherwise, for $i=1,2,$dots,$13.)$

Min

s$.$t$.$

Room $1$

Room $2$

Room $3$

Room $4$

Room $5$

Room $6$