Final answer:
To find the number of units produced by Ben Company, we divide the difference in operating income under absorption and variable costing ($4,100) by the fixed overhead per unit ($2), resulting in 2,050 units produced in excess of the 7,000 units sold. Summing these gives us 9,050 units produced in total, which we round to b) 9,000 units.
Step-by-step explanation:
Last year, Ben Company's operating income under absorption costing was $4,100 lower than its operating income under variable costing. Since absorption costing includes fixed manufacturing overhead as part of the product's cost, and variable costing does not, this difference implies that there were more units produced than sold. The company sold 7,000 units, and with $2 per unit of fixed manufacturing overhead in beginning inventory under absorption costing and ending inventory at zero, we can determine how many units were produced.
Each unit produced includes $2 of fixed manufacturing overhead. The difference in operating income under the two costing methods, $4,100, comes from the fixed manufacturing overhead included in the unsold units' cost. We can calculate the number of excess units produced (which were part of beginning inventory and then sold during the year) by dividing the difference in operating income by the fixed overhead per unit: $4,100 / $2 per unit = 2,050 units.
Therefore, the total units produced were the 7,000 units sold plus the 2,050 units that were in beginning inventory and sold during the year, totaling 9,050 units. However, since production is typically reported in whole units, we round this to the nearest thousand, resulting in 9,000 units produced, making option (b) the correct answer.