Final answer:
To find the manufacturing overhead, calculate the total conversion costs using the direct labor and the overhead percentage. Manufacturing overhead is 20% of the total conversion costs. The correct answer to the student's question, based on the direct labor cost of $45,000, is A) $11,250.
Step-by-step explanation:
The student's question pertains to calculating manufacturing overhead based on given conversion cost percentages and cost figures for direct labor and materials. To compute the manufacturing overhead, we need to determine the total conversion costs first, which consist of direct labor and manufacturing overhead, given that direct materials are not part of conversion costs. Since we know that manufacturing overhead is 20% of the conversion cost, we can set up an equation with direct labor as a known variable to find the overhead cost:
Manufacturing Overhead = 20% of Conversion Costs
Conversion Costs = Direct Labor + Manufacturing Overhead
Let's denote Manufacturing Overhead as MO and Conversion Costs as CC. So, MO = 20% of CC, meaning MO = 0.20 * CC. We are given Direct Labor (DL) as $45,000. We know that CC = DL + MO which means CC = $45,000 + MO. Substituting the value of MO in terms of CC, we get CC = $45,000 + 0.20 * CC. Solving for CC, we will find the total Conversion Costs. Once CC is found, we can easily calculate MO, which is 20% of the CC. Upon solving the equation, we will arrive at MO being $11,250. Therefore, the correct answer to the student's question is A) $11,250.