This answer results from assuming that all of the additional production will be sold. The problem does not say that the additional production will be sold. The expected sales are still only 5,000 units, and only the revenues and costs for units that are sold reach the income statement. Only the production increases, and that causes an increase to inventory on hand. Because the production increases, the amount of fixed overhead applied to production will be more than the actual incurred fixed overhead. That variance will be closed out by crediting the amount of the overapplication to cost of goods sold, which will increase gross profit and increase net income before taxes by the amount of the variance. However, this answer would result in an increase in net income before tax of only $4,920, which would not accomplish George's misguided goal.
The company is expecting $20,000 in operating income, and George wants to increase that by $30,000 to $50,000. Both sales and production are planned for 5,000 units. Budgeted fixed manufacturing cost is $100,000, so the application rate for fixed overhead is $20 per unit ($100,000 ÷ 5,000 units expected to be produced). If the company increases production above what it can sell, inventory will increase. As a result, the fixed manufacturing cost applied to the unsold units in inventory will be on the balance sheet instead of in Cost of Goods Sold on the income statement, and net income will be increased by the amount of fixed manufacturing cost attached to the unsold units in ending inventory. To increase net income by $30,000, the number of units in inventory will need to increase by $30,000 ÷ $20 fixed manufacturing cost applied per unit, or 1,500 units. The company's practice is to write off under- or over-applied manufacturing cost to COGS. If production is increased by 1,500 units, fixed manufacturing cost will be overapplied by 1,500 units × $20 per unit, or $30,000, assuming that actual fixed manufacturing cost is the same as budgeted fixed manufacturing cost. This overapplied fixed manufacturing cost will be cleared out at the end of the period with a credit to COGS of $30,000. So fixed manufacturing cost in COGS will be $30,000 lower than it would have been if the company had produced only the 5,000 units it planned to produce and that it was able to sell. Note that because the whole variance is written off (credited) to Cost of Goods Sold, Finished Goods Inventory will not be adjusted. That extra $30,000 will remain on the balance sheet in Inventory at year end, still attached to the 1,500 extra unsold units that were produced. Because of the overproduction which led to a variance and the resulting credit to Cost of Goods Sold expense, only $70,000 of the actual $100,000 of fixed manufacturing cost incurred will reach the income statement, whereas all $100,000 of it would reach the income statement if only 5,000 units were produced and sold. When in some future year the company cuts production in order to sell down the extra inventory it built up this year, each unit produced in that future year will bear more of that year's fixed overhead. Cost of goods sold for that future year will include the $30,000 from this year's fixed overhead (for the units sold out of inventory) plus the greater amount of fixed overhead per unit for the units sold from the future year's decreased production. As a result, cost of goods sold in that future year will be higher than it should be and net income will be lower than it should be. Thus the result of the overproduction in the current year is to move some of a future year's net income into the current year.
This answer results from including fixed selling and administrative cost along with fixed manufacturing cost in the calculation. Only fixed manufacturing cost is relevant.
This answer results from (1) assuming that current budgeted operating income is zero and operating income is to be increased by the full $50,000 of desired operating income instead of by $30,000; and (2) misreading the question as asking for the total number of units to be produced instead of the increase in the number of units to be produced.
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