A substantial part of United Parcel Service$$s freight traffic moves as a trailer$-$on$-$flatcars $($i$.$e$.$

with truck trailers travelling most of the way on railroad flatcars$).$ The required number of

truckloads di$,$j

to be shipped between points i$,$ j $=1,2,,...,$ n in this way is known, but UPS

can use either its own trailer at unit cost ci$,$j

or rent trailers from railroad company at unit cost

ri$,$j

$.$ Rented trailers can be left anywhere, but UPS wishes to balance the number of its own

trailers available at every point. That is$,$ the number of company trailers inbound at any point

should be equal the number outbound. If necessary, trailers may be returned empty from i to j at

unit cost ei$,$j

to meet this requirement. Develop an optimization model to find a minimum total

cost shipping plan.

Check if your model is a $($single commodity$)$ network flow problem. If$,$ yes how $($identify the

arcs, flow, capacity etc.$)?$