A team of archaeologists are working on a site in South America. Over the past few months a number of interesting discoveries have been made. All the discoveries lay within a grid which is 1000 square metres in size. The coordinates of each dig site are given in attached file.
The dig sites have started to reveal an increasingly large number of artefacts. The site manager would like to build a headquarters within the 1000 m2 grid where all the new discoveries can be collected and examined. To reduce complaints from workers he would like to position the new building in such a way that the total distance from the headquarters to all sites is at a minimum. The distance between a particular dig site and the headquarters can be found using the equation below.
SQRT((Xhq-Xs)^2 + (Yhq-Ys)^2)
What is the coordinates of the best position of the new headquarters?
More details of the problem see attached file