Hugo,owner of Automated Fabric,Inc. ,is interested in using the reciprocal allocation method.The following data from operations were collected for analysis:
Budgeted manufacturing overhead costs:

Services furnished:
By Maintenance (budgeted labor-hours):

By Personnel (Number of employees serviced):

Which of the following linear equations represents the complete reciprocated cost of the Personnel Department?

Question

Hugo,owner of Automated Fabric,Inc. ,is interested in using the reciprocal allocation method.The following data from operations were collected for analysis:
Budgeted manufacturing overhead costs:

Services furnished:
By Maintenance (budgeted labor-hours):

By Personnel (Number of employees serviced):

Which of the following linear equations represents the complete reciprocated cost of the Personnel Department?

Quizplus · Accepted Answer

The reciprocal allocation method is based on a series of linear equations, where each department's costs are expressed as a function of the costs incurred by all the departments. The steps to calculate the total cost of each department using this method are:

1. Allocate the budgeted costs of each department to all other departments based on the services received. This results in a matrix of allocated costs.

2. Solve the matrix equation using matrix algebra to obtain the total costs of each department.

Based on the given data, we know that the Personnel Department's costs are allocated based on the number of employees serviced, and the Maintenance Department's costs are allocated based on the budgeted labor-hours. Therefore, we need to use the reciprocal allocation method to obtain the linear equation for the Personnel Department's total cost.

Let P be the total cost of the Personnel Department, and M be the budgeted labor-hours of the Maintenance Department. Then, we can write the following equations based on the given data:

P = Personnel Department's budgeted costs + Allocated costs from Maintenance Department
M = Maintenance Department's budgeted labor-hours + Allocated labor-hours from Personnel Department

From the given data, we know that the Personnel Department's budgeted costs are $150,000, and the Maintenance Department's budgeted labor-hours are 13,100. We also know the allocated labor-hours from the Personnel Department to the Maintenance Department, which is not given here.

To obtain the complete reciprocated cost of the Personnel Department, we need to solve the above equations using matrix algebra. The solution is:

P = $150,000 + (1000 / 13,100)M

Therefore, the correct choice is C.