The "straight$-$line" distance between two cities $in$ the United States can $be$ approximated $by$ the following formula, where $la{t}_1$ and $\frac{?}{on{g}_1}$ are the latitude and longitude $of$ city $1$ and $\frac{?}{a{t}_2}$ and $lon{g}_2$ 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.

$69\sqrt[\phantom{2}]{(\text{l}\text{a}\text{t}{?}_{(}()()1)-\text{l}\text{a}\text{t}{?}_{(}()()2){)}^2+(\text{l}\text{o}\text{n}\text{g}{?}_{(}()()1)-\text{l}\text{o}\text{n}\text{g}{?}_{(}()()2){)}^2}$

Ted's daughter $is$ getting married, and $heis$ 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. 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