A portable lunch wagon is to be located along the main aisle of an industrial plant. On a coordinate system, the main aisle connects the points (0, 10) and (12, 10). Travel between customer locations and the main aisle is rectilinear. The coordinate points for the locations of workstations served by the lunch wagon are as follows: P1 = (2, 4); P2 = (2, 12); P3 = (6,4); P4 = (6,12); P5 = (8,8); P6 = (12,12); P7 = (10,14); P8 = (12,6); P9 = (8,14); and P10 = (10, 4).

(a) If a single customer is located at each workstation, where should the lunch wagon be located along the main aisle to minimize cumulative customer walking distance? Formulate the problem and solve for the optimum location using the half-sum method.

(b) If one customer is located at each of the first five workstations, and three customers are located at each of the last five workstations, where should the lunch wagon be located along the main aisle? Formulate the problem and solve for the optimum location using the half-sum method.

(c) If it is desired to locate the lunch wagon such that the maximum distance traveled by any customer is minimized, where should the lunch wagon be located?