A new machine will be installed that interacts with 5 existing ones: Use straight distance. a) If there is no restriction on where the new machine can be located and we wish to minimize the sum of the flows times the distance traveled, where would you recommend locating the new machine (15 pts) b) If there are only two possible locations, these are (10,10) and (20,15), which would you choose? Justify it numerically. (15 points) c) If we forget about the flows, where a new machine should be located so that the distance to the furthest machine is minimized. (15 points)