To calculate the Fabrication Department's factory overhead rate, we will use the following formula:

$\text{Factory Overhead Rate} = \frac{\text{Total Factory Overhead}}{\text{Total Machine Hours}}$

Step 1: Calculate the total machine hours for each product.

• Rings: 1,140 units × 9 machine hours/unit = 10,260 machine hours
• Dings: 1,860 units × 11 machine hours/unit = 20,460 machine hours

$\text{Total Machine Hours} = 10,260 \, \text{(Rings)} + 20,460 \, \text{(Dings)} = 30,720 \, \text{machine hours}$

Step 2: Use the formula to calculate the Fabrication Department's overhead rate.

$\text{Fabrication Department's Overhead Rate} = \frac{\text{Total Factory Overhead in Fabrication}}{\text{Total Machine Hours in Fabrication}} = \frac{81,900}{30,720}$

$\text{Fabrication Department's Overhead Rate} = 2.67 \, \text{per machine hour}$

Thus, the correct answer is:

c. $2.67 per machine hour

Let me know if you need any additional details or have further questions!

Here are 5 related questions you might find useful:

1. How do we calculate the overhead rate for the Assembly Department?
2. How would the overhead rate change if the total factory overhead increased in the Fabrication Department?
3. How do you allocate factory overhead to individual products using these rates?
4. What would happen to the total overhead cost if the number of units produced for Rings increased?
5. How do you apply the factory overhead rates to determine the total overhead cost for each product?

Tip: When calculating factory overhead rates, always check the allocation base (machine hours or labor hours) for each department to ensure you're dividing by the correct quantity.