Suppose that one wishes to schedule vehicles from a central depot to five customer locations. The cost of making trips between each pair of locations is given in the following matrix. (Assume that the depot is location 0.)

Assume that these costs correspond to distances between locations and that each vehicle is constrained to travel no more than 50 miles on each route. Find the routing suggested by the savings method.

Cost Matrix (cij) \begin{tabular}{lccccccc} \hline & & & TO & & \\ \hline & & 0 & 1 & 2 & 3 & 4 & 5 \\ & 0 & & 20 & 75 & 33 & 10 & 30 \\ F & 1 & & 35 & 5 & 20 & 15 \\ R & 2 & & & 18 & 58 & 42 \\ O & 3 & & & 40 & 20 \\ M & 4 & & & & 25 \\ \hline \end{tabular}