In the following problem, help was given by the chart below. What is the Normalized weight column? How was that determined? How does that help to solve the problem?

4. \#15. A machine shop has five machines, located at (3,3),(3,7),(8,4),(12,3), and (14,6), respectively. A new machine is to be located in the shop with the following expected numbers of loads per hour transported to the existing machines: 1/8,1/8,1/4,1, \& 1/6. Material is transported along parallel aisles, so a rectilinear distance measure is appropriate. (5 pts) A. Find the coordinates of the optimal location of the new machine to minimize the weighted sum of the rectilinear distances from the new machine to the existing machines. (The optimal value of the x coordinate is found by dividing the total cumulative weight by 2 and identifying the first location at which the cumulative weight exceeds this value.) (The optimal value of the y coordinate is found by dividing the total cumulative weight by 2 and identifying the first location at which the cumulative weight exceeds this value.)