The "straight$-$line" distance between two cities in the United States can be approximated by the following formula, where lat, and long, are the latitude and longitude of city $1$ and latz and long, 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:

Click on the datafile logo to reference the data.

DATA file

$69($lat$-$lata$)+($long$,$ long$)$

Ted's daughter is getting married, and he is inviting relatives from $15$ different locations in the United States. The DATAfile Wedding gives the longitude, latitude, and number of relatives in each of the $15$ locations. 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. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even. $($Example: $-300)$ Do not round intermediate calculation.

Latitude of the optimal wedding location

Longitude of the optimal wedding location$=$

Total demand$-$weighted distance