Question

Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow:

				Proportion of Services Used by
Department	Direct Costs			Maintenance		Cafeteria		Machining		Assembly
Machining	$	140,000
Assembly		68,000
Maintenance		52,000		—		0.3		0.3		0.4
Cafeteria		33,000		0.8		—		0.1		0.1

Required:

Use the reciprocal method to allocate the service costs. (Matrix algebra is not required.) (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

	Maintenance	Cafeteria	Machining	Assembly
Service Department Costs
Maintenance
Cafeteria
Total

Thank You!

Answer 1

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Caro Manufacturing
Reciprocal Method	Maintenance	Cafeteria	Machining	Assembly	Total
Maintenance		0.30	0.30	0.40	1.00
Cafeteria	0.80		0.10	0.10	1.00
Direct Costs	52,000.00	33,000.00	140,000.00	68,000.00	293,000.00
Let Total cost of Maintenance is $ X and Total cost of Cafeteria is $ Y
So, X= 52000+ 0.80 of Y	Equation 1
Y= 33000+ 0.30 of X	Equation 2
Or, X= 52000+ 0.80Y
Y= 33000+ 0.30X
Substituting the value of X in equation 2:
Y = 33000 + 0.30(52,000 + 0.80Y)
Y = 33000 + 15,600+0.24Y
Y – 0.24Y = 33000 + 15,600
0.76Y= 48600
Y = 48600/0.76
Y = $ 63,947.37
Substituting the value of Y in equation 1:
So, X= 52000+ 0.80 of Y
So, X= 52000+ 0.80 of 63,947.37
So, X= 52000+ 51157.89
So, X= 103,157.89
Allocation Summary	Maintenance	Cafeteria	Machining	Assembly	Total
Maintenance		0.30	0.30	0.40	1.00
Cafeteria	0.80		0.10	0.10	1.00
Direct Costs	52,000.00	33,000.00	140,000.00	68,000.00	293,000.00
Allocation
Human Resources	(103,157.89)	30,947.37	30,947.37	41,263.16	-
General Factory	51,157.89	(63,947.37)	6,394.74	6,394.74	-
Total cost after allocation	0.00	(0.00)	177,342.10	115,657.89	293,000.00