The company collaborates with facilities in seven different states. The location information of these facilities has been converted into the following coordinate scale in the table below:

$$ Fn: means Facility ID

$($X$,$ Y$)$ coordinates

Facility # State Coordinates

F$1$ Indiana $(4\mathrm{.}8,4\mathrm{.}0)$

F$2$ Kentucky $(5\mathrm{.}0,3\mathrm{.}5)$

F$3$ Michigan $(5\mathrm{.}0,5\mathrm{.}5)$

F$4$ Mississippi $(4\mathrm{.}5,2\mathrm{.}0)$

F$5$ Missouri $(4\mathrm{.}0,4\mathrm{.}0)$

F$6$ North Carolina $(6\mathrm{.}0,3\mathrm{.}5)$

F$7$ Tennessee $(5\mathrm{.}0,3\mathrm{.}0)$

You are tasked with identifying a location for a new warehouse that minimizes transportation costs to these nine facilities. The cost of transportation per unit distance will be the same between the new warehouse and other facilities. However, the number of trips per day between the warehouse and other facilities, F$1,$ F$2,$ F$3,$ F$4,$ F$5,$ F$6,$ and F$7,$ are $15,20,10,5,25,18,$ and $7,$ respectively.