The optimal total shipping cost in a minimization transportation model is $622, and the reduced cost from source node 1 to destination node 6 is $6. This implies that if one were to deviate from the optimal solution by shipping one unit from node 1 to node 6, the new minimum total shipping cost would be $628

True or False

true

True

To determine whether the statement is true or false, we need to understand the concept of reduced cost in a transportation model and how it relates to the total shipping cost.

In a transportation model, the reduced cost represents the amount by which the total shipping cost would decrease if one unit of shipment is added between a source and destination. Naturally, the reduced cost is negative if the addition of the shipment reduces the overall cost.

Given that the reduced cost from source node 1 to destination node 6 is $6, it implies that adding one unit of shipment from node 1 to node 6 would decrease the total shipping cost by $6. Therefore, the new minimum total shipping cost would be $622 - $6, which equals $616.

Since the statement suggests that the new minimum total shipping cost would be $628, which contradicts our calculation above, the statement is FALSE.

Therefore, the correct answer is: False.