Mark and His Friends Are Planning for a Holiday Party

Mark and his friends are planning for a holiday party. Data on longitude, latitude, and number of friends at each of the 10 locations are given below. Mark would like to identify the location for the holiday party such that it minimizes the demand-weighted distance, where demand is the number of friends at each location. Find the optimal location for the party. The distance between two cities can be approximated by the following formula. $$50 \sqrt { \left( \text { lat } _ { 1 } - \text { lat } _ { 2 } \right) ^ { 2 } + \left( \text { long } _ { 1 } - \text { long } _ { 2 } \right) ^ { 2 } }$$ where lat1 and long1 are the latitude and longitude of city 1, and lat2 and long2 are the latitude and longitude of city 2. (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.) $$\begin{array} { l | c | c | c } \text { Location } & \text { latitude } & \text { longitude } & \text { Friends } \\\hline \text { Ohio } & 26.782 & - 77.639 & 12 \\\text { TN } & 38.952 & - 76.164 & 2 \\\text { Mass } & 36.961 & - 85.921 & 1 \\\text { Iowa } & 33.216 & - 81.753 & 8 \\\text { New York } & 36.499 & - 84.575 & 10 \\\text { Virginia } & 44.934 & - 72.798 & 7 \\\text { NJ } & 40.850 & - 76.657 & 5 \\\text { Wyoming } & 42.901 & - 75.514 & 6 \\\text { Maryland } & 41.019 & - 120.491 & 1 \\\text { CA } & 43.623 & - 119.626 & 9\end{array}$$