The AB Company produces two products, \(\mathrm{A}\) and \(\mathrm{B}\), in two separate departments. In addition, the company has two service departments ( \(\mathrm{X}\) and \(\mathrm{Y}\) ) providing service to the production departments in manufacturing Products \(\mathrm{A}\) and \(\mathrm{B}\). An analysis of the service provided by Departments \(\mathrm{X}\) and \(\mathrm{Y}\) in a period is as follows:

Required:
Determine the allocation of service costs to Production Departments A and B using:
(1) The Direct Method (2) The Step Method (allocate Service Department Y's costs first)
(3) The Linear Algebra Method

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To From X Y A B Total Services Provided (Units) XY 0 20 50 30 100 0 100 50 200 50 Service costs to be allocated are: Department X Y Amount $ 2,000 10,000