Question

University Printers has two service departments (Maintenance and Personnel) and two operating departments (Printing and Developing). Management has decided to allocate maintenance costs on the basis of machine-hours in each department and personnel costs on the basis of labor-hours worked by the employees in each.

The following data appear in the company records for the current period:

	Maintenance			Personnel			Printing			Developing
Machine-hours		—			1,000			1,000			3,000
Labor-hours		500			—			500			2,000
Department direct costs	$	5,000		$	12,000		$	15,000		$	10,000

Required:

Allocate the service department costs using the reciprocal method. (Matrix algebra is not required because there are only two service departments.) (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your final answers to the nearest whole dollar amounts.)

Answer 1

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	To
From	Maintenance	Personnel	Printing	Developing
Service Departmentl costs	$             5,000	$        12,000
Maintenance allocation	$           -7,241	$           1,448	$         1,448	$           4,345
Personnel allocation	$             2,241	$       -13,448	$         2,241	$           8,965
Total Cost	$                     0	$                   0	$         3,690	$         13,310
Note: Must include minus sign while posting answer
Workings:
Let Total Service department cost of Maintenance be x and ofPersonnel be y
x = $5000 + (500/3000 * y)
y = $12000 + (1000/5000 * x)
By solving above:
y = $12000 + (1000/5000 * x)
y = $12000 + [1000/5000 * ($5000 + (500/3000 * y)]
y = $13448
also,
x = $5000 + (500/3000 * y)
x = $5000 + (500/3000 * $13448)
x = $7241