Final answer:
The carrying value of the ending inventory under variable costing for the Southern Corporation would be $6,400, calculated as 200 units of unsold inventory multiplied by the variable cost of $32 per unit.
Step-by-step explanation:
The carrying value of the ending inventory under variable costing will include only the variable costs associated with the production of the inventory. Since there was no beginning inventory and the number of units produced was different from the number of units sold, the ending inventory is the difference, which is 5,810 units produced minus 5,610 units sold, equaling 200 units. Under variable costing, only variable production costs are included in inventory valuation, which is $32 per unit in this case.
Hence, the carrying value of the ending inventory under variable costing would be 200 units x $32 variable cost per unit, which equals $6,400.