Question

Midland Resources has two production departments (Fabrication and Assembly) and three service departments (Engineering, Administration, and Maintenance). During July, the following costs and service department usage ratios were recorded.

Supplying Department	Using Department
	Engineering			Administration			Maintenance			Fabrication			Assembly
Engineering		0			40	%		0			15	%		45	%
Administration		20	%		0			25	%		45	%		10	%
Maintenance		0			30	%		0			15	%		55	%
Direct cost	$	42,000		$	248,550		$	45,000		$	230,000		$	80,000

Required:

Allocate the service department costs to the two operating departments 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.)

	Cost Allocation To: From: Maintenance Personnel Printing Developing Service department costs Maintenance Personnel Total $0 $0 $0 $0

Answer 1

	Allocated to:
From	Costs	Fabrication	Assembly
Engineering	$      1,08,000	$       16,200	$     48,600
Administration	$      3,30,000	$   1,48,500	$     33,000
Maintenance	$      1,27,500	$       19,125	$     70,125
Total Cost		$   1,83,825	$ 1,51,725
Workings:
Let Total Engineering department cost be x and of Administration be y and of Maintenance be z
x = 42000 + (0.20 y)
y = $248550 + (0.40 x) + (0.30 z)
z = 45000 + (0.25 y)
By solving above:
y = $248550 + [0.40 (42000 + (0.20 y))] + [0.30 (45000 + (0.25 y))]
y = $330000
also,
x = 42000 + (0.20 * $330000)
x = $108000
and,
z = 45000 + (0.25 * $330000)
z = $127500