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			50	%		0			10	%		40	%
Administration		10	%		0			20	%		50	%		20	%
Maintenance		0			50	%		0			20	%		30	%
Direct cost	$	24,000		$	179,500		$	25,000		$	185,000		$	50,000

  
Required:

Allocate the service department costs to the two operating departments using the reciprocal method. (Do not round intermediate calculations.)

	Costs	Fabrication	Assembly
Engineering	?	?	?
Administration	?	?	?
Maintenance	?	?	?
Total

Answer 1

SOLUTION

Equation:Enginnering (X) ,Administration (y ) and maintenance(z)

Enginnering dept. total cost ((x) = 24000 + .10 y             [Equation 1]

Administration dept. cost (y): 179500+ .50x +.50z            [Equation 2]

Maintenance dept. cost (z): 25000+ .20y                      [Equation 3]

Putting value of equation 1 & equation 3 in equation 2

y= 179500+ .50 (24000+.10y)+.50(25000+.20y)

y= 179500+12000+.05 y+12500+.1y

y-.05y-.1y= 204000

y= 204000/.85 = 240,000

x= 24000+ (.10*240000) = 48,000

z=25000+.20 (240000)=25000+48000=73,000

	Cost	Fabrication	Assembly
Engineering	48,000	4800 [48,000*.10]	19,200 [48000*.40]
Administration	240,000	120,000 [240000*.50]	48,000 [240000*.20]
Maintenance	73,000	14,600   [73000*.20]	21,900 [73000*.30]
Total		139,400	89,100