A portable lunch wagon is to be located along the main aisle of an industrial plant. The vendor wishes to locate the wagon so that the total walking distance for his customers is minimized. On a coordinate system the main aisle runs parallel to the x-axis at y = 10. Workstations are located at the following coordinate points. Travel from the workstations to the main aisle is rectilinear.

Station Location

1 (4,4)

2 (4,12)

3 (6,4)

4 (6,12)

5 (8,8)

6 (12,12)

7 (10,4)

8 (12,6)

9 (8,14)

10 (10,14)

a) If one customer is located at each station, where should the wagon be located along the main aisle to minimize cumulative walking distance?

b) If one customer is located at stations 1, 2, 3, 4 and 5 (i.e, one customer for each station, 5 customers in total), and three customers are located at stations 6, 7, 8, 9 and 10 (i.e, three customers for each station, 15 customers in total), where should the wagon to be located along the main aisle to minimize cumulative customer walking distance?

c) The vendor decided that he can serve better if he uses two lunch wagons instead of only on wagon. Meanwhile, the management of the industrial plant decided to reconsider the placement of the service facilities. Now, the vendor is allowed to place the lunch wagons only on those points with even integer coordinate values (e.g. 0, 2, 4, ...). Using the demand values given in part (b), what is the best pair of locations for the wagons on the main aisle, if the vendor places two wagons instead of one, considering the new regulations? (Hint: Use multiple facility location approach after determining the potential points.)