# Question

Suppose that the air freight charge per ton between seven particular locations is given by the following table (except where no direct air freight service is available):

A certain corporation must ship a certain perishable commodity from locations 1–3 to locations 4–7. A total of 70, 80, and 50 tons of this commodity is to be sent from locations 1, 2, and 3, respectively. A total of 30, 60, 50, and 60 tons is to be sent to locations 4, 5, 6, and 7, respectively. Shipments can be sent through intermediate locations at a cost equal to the sum of the costs for each of the legs of the journey. The problem is to determine the shipping plan that minimizes the total freight cost.

(a) Describe how this problem fits into the format of the general transshipment problem.

(b) Reformulate this problem as an equivalent transportation problem by constructing the appropriate parameter table.

A certain corporation must ship a certain perishable commodity from locations 1–3 to locations 4–7. A total of 70, 80, and 50 tons of this commodity is to be sent from locations 1, 2, and 3, respectively. A total of 30, 60, 50, and 60 tons is to be sent to locations 4, 5, 6, and 7, respectively. Shipments can be sent through intermediate locations at a cost equal to the sum of the costs for each of the legs of the journey. The problem is to determine the shipping plan that minimizes the total freight cost.

(a) Describe how this problem fits into the format of the general transshipment problem.

(b) Reformulate this problem as an equivalent transportation problem by constructing the appropriate parameter table.

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