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 lat$2$ 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.

$69$

$($lat$1$ lat$2)2+($long$1$ long$2)2$

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.

Location lat long # Relatives

NewYork $40\mathrm{.}714352874\mathrm{.}005973144$

Maryland $39\mathrm{.}025665177\mathrm{.}07636697$

Virginia $37\mathrm{.}431573478\mathrm{.}65689422$

SC $32\mathrm{.}216316080\mathrm{.}75260801$

NC $35\mathrm{.}772096078\mathrm{.}638614511$

TN $35\mathrm{.}960638483\mathrm{.}92073921$

FL $27\mathrm{.}498927882\mathrm{.}57481945$

Ohio $39\mathrm{.}136111084\mathrm{.}50305567$

Wyoming $43\mathrm{.}6226250110\mathrm{.}62605901$

CA $34\mathrm{.}0194543118\mathrm{.}49119129$

Iowa $41\mathrm{.}698611193\mathrm{.}04694446$

IL $41\mathrm{.}850033087\mathrm{.}65005233$

Mass $42\mathrm{.}933979270\mathrm{.}79838551$

NJ $40\mathrm{.}901210174\mathrm{.}51432329$

PA $39\mathrm{.}952335075\mathrm{.}16378902$

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