Ten workstations are located as shown on a tree network (the tree network can be interpreted as the aisles of the facility). The length of each line segment on the tree is given in the figure. The weights between the existing facilities and the new facility to be located are also provided (in red color). Determine the optimum location for the new facility on the tree using a minisum criterion (i.e. solve the 1-median problem). You can use either the Chinese method or the majority method. 15 W = 3 . 2 1 w = 5 W4 W, = 2 4 2 4 4 2 2 10 2 2 3 . v-axis 2 w 2 2 . W10 3 W3 = 3 4 4 3 . W, = 2 Ws = 4 Wg = 6 5 1 10 15 X-axis Hint: You don't have to draw the whole tree repeatedly for each iteration of your method. Just draw the tree with the vertices that need to be added once. Then, give a list of the trimming operations that need to be conducted (e.g. Trim vertex a upon vertex b. The new value of w becomes c.) Finally, indicate the optimal location of the new facility on the tree that you draw