A transportation problem is a linear optimization problem, which seeks to minimize the total transportation cost from the origins to the destinations. The total cost is the sum of the total cost of each route, which is the multiplication of the unit cost with the amount of the units to be transported on the respective route. The decision variables of this problem are the amounts of shipment, as the transportation costs are given data. A balanced transportation model is a linear model with equality constraints. The inverse of a linear problem can be modeled as the dual of the original model. The dual of a balanced transportation problem is interpreted as a problem of a counterpart who provides an alternative to transportation. The decision variables of the dual model are the prices of the alternative service offered by the counterpart actor. At the optimum point, the objective value of the primal and the dual models are the same, and the optimum solution is the only solution that meets the restrictions for both models. Hence, the optimality of a basic feasible solution for the transportation model can be tested by checking the feasibility of the dual solution. The correct answer is B.