You are asked to locate security cameras in a football stadium. There are $8$ potential

locations for these cameras, in each location covers certain areas of the stadium, as given in

the table below:

Camera

location

$12345678$

Stadium

area

$1,3,4,$

$6,7$

$4,7,8,$

$12$

$2,5,9,$

$11,13$

$1,2,$

$14,15$

$3,6,$

$10,12,$

$14$

$8,14,$

$15$

$1,2,6,$

$11$

$1,2,4,$

$6,8,$

$12$

a$)$ Formulate the problem as a set covering model and find the smallest number of cameras so

that each stadium area is covered.

b$)$ The security manager of the stadium told you that some stadiums are $$critical$$ in terms of

security, and he would like to have as many cameras as possible covering these critical areas.

He believes if a critical area is covered by multiple cameras, he can identify offenders with

higher certainty. Create a Pareto frontier that gives the number of cameras installed along

the x$-$axis and the number of cameras covering the critical areas along the y$-$axis $($the chart is

ready, you just need to enter the data in cells P$3$:Q$6)$