Marion County is trying to determine where to place the county$$s animal rescue shelter. The locations of the county$$s four major towns are, respectively, as follows: $(110,240),(619,270),(405,382)$ and $(812,657)($when placed on a Cartesian coordinate system; see the following chart$).$

Town $1$ averages $200$ rescues per year; town $2$ average $300$ rescues; town $3$ averages $400$ rescues; and town $4$ averages $250$ rescues. The county wants to build the shelter in a location that minimizes the average distance that a rescue vehicle must travel to respond to a rescue. Because most roads in the county run in either an east$-$west or a north$-$south direction, the rescue vehicles must do the same. For

example, if the rescue station is located at $(355,611)$ and a rescue occurs at town $1,$ the rescue engine has to travel$|110-355|+|240-611|=616$ miles to the rescue. This is called the $$taxicab$$ metric and is a more accurate way to measure city travel distances than the classic $$Euclidean distance$$ formula used in geometry. PLEASE FIND THE OPIMAL SOLUTION ONLY USING EXCEL AND SOLVER. PLEASE LAY OUT THE OBJECTIVE, DECISION VARIABLES, AND CONSTRAINTS AND SHOW ALL STEPS. THANK YOU.