Final answer:
The carrying value of the ending inventory under variable costing is calculated by adding the variable production cost per unit to the variable selling and administrative cost per unit, then multiplying by the remaining inventory units, resulting in a value of $9,800.
Step-by-step explanation:
To calculate the carrying value of the ending inventory under variable costing, we only consider the variable costs that are directly tied to the production of the goods. Since the Southern Corporation produced 6,230 units and sold 6,030 units, there is an ending inventory of 200 units (6,230 produced - 6,030 sold). The variable costs per unit consist of production costs at $33 and selling and administrative costs at $16. Therefore, the carrying value of the ending inventory is the variable production cost per unit plus the variable selling and administrative cost per unit, multiplied by the number of units remaining in inventory.
The calculation would be: (33 + 16) * 200 = $49 * 200 = $9,800.
Thus, the carrying value on the balance sheet of the ending inventory under variable costing would be $9,800.