Problem $2.$ Facility Location Problem $(6$ points$)$

Mr$.$ Gordon wishes to locate a police station in an attempt to reduce the crime rate in the three most

dangerous zones of the city. The following table presents the position of a central location within each zone

Zone Index $$

$($x$-$axis$)$

$($y$-$axis$)$

$1412$

$282$

$31410$

$2-1.$ Using $1-$norm distance, please develop the full optimization model to locate the police station. You

need to show $1)$ decision variables, $2)$ constraints, and $3)$ the objective function.

$2-2.$ Each zone has different danger levels, as given below. The more dangerous the area, the closer the

police station must be located. How will the optimization model be changed?

Zone Index Danger Level $($

$)$

$14$

$22$

$32$