The transportation problem, as it was formulated at the beginning of this chapter, is a minimization problem just as the one exemplified for the economic interpretation of the dual model. However, the difference is that the constraints of the transportation model are in the form of equality. Thus, the duality relation here is asymmetric.

The dual model interchanges costs and constraints of the primal model, and converts the objective from maximization to minimization. Hence, there is a dual variable y for each constraint. In the case of the transportation model, the dual variable y is defined with a pair of variables; u, for the constraints of origins and v, for the constraints of destinations.

The dual of the transportation model can be interpreted as the dual model explained in the previous subsection. For the problem of the production decision, a counterpart actor was assumed as if it provided a purchasing alternative. A similar assumption can be made to interpret the dual of the transportation model. The original problem is to select the most economical distribution routes that meet the demands of the destinations. Total cost of the shipment depends on total costs of transportation for the selected routes. The decision variables for the primal model are the amounts to be carried from the origins (e.g. production locations) to the destinations (e.g. retailing locations).

According to these information, the correct answer is option E.