$316/17$

The "straight$-$line" distance between two cities in the United States can be approximated by the following formula, where lat ${?}_1$ and long ${?}_1$ are the latitude and longitude of city $1$ and $la{t}_2$ and long $2$ are the latitude and longitude of city $2,$ and the value $69$ corresponds to the number of miles in a degree of latitude or longitude.

$)1)2)1$

Ted's daughter is getting married, and he is inviting relatives from $15$ different locations in the United States. The table below gives the longitude, latitude, and number of relatives in each of the $15$ locations.

$\backslash$table$[[$Location$,$lat,long,# Relatives$],[$New York,$40\mathrm{.}7143528,-74\mathrm{.}0059731,42],[$Maryland$,39\mathrm{.}0256651,-77\mathrm{.}0763669,7],[$Virginia$,37\mathrm{.}4315734,-78\mathrm{.}6568942,2],[$SC$,32\mathrm{.}2163160,-80\mathrm{.}7526080,1],[$NC$,35\mathrm{.}7720960,-78\mathrm{.}6386145,11],[$TN$,35\mathrm{.}9606384,-83\mathrm{.}9207392,1],[$FL$,27\mathrm{.}4989278,-82\mathrm{.}5748194,7],[$Ohio$,39\mathrm{.}1361110,-84\mathrm{.}5030556,7],[$Wyoming$,43\mathrm{.}6226250,-110\mathrm{.}6260590,1],[$CA$,34\mathrm{.}0194543,-118\mathrm{.}4911912,11],[$Iowa$,41\mathrm{.}6986111,-93\mathrm{.}0469444,6],[$IL$,41\mathrm{.}8500330,-87\mathrm{.}6500523,5],[$Mass$,42\mathrm{.}9339792,-70\mathrm{.}7983855,1],[$NJ$,40\mathrm{.}9012101,-74\mathrm{.}5143232,11],[$PA$,39\mathrm{.}9523350,-75\mathrm{.}1637890,2]]$

Ted would like to find a wedding location that minimizes the demand$-$weighted distance, where demand is the number of relatives at each location. Assuming that the wedding can occur anywhere, find the latitude and longitude of the optimal location. $($Hint: Notice that all longitude values given for this problem are negative. Make sure that you do not check the option for Make Unconstrained Variables Non$-$Negative in Solver. Round your answers to three decimal places.$)$

latitude of the optimal wedding location

longitude of the optimal wedding location