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The following is a system of simultaneous linear equations to allocate costs using the reciprocal method. Matrix algebra is not required.The following costs were incurred in three operating departments and three service departments in Westmoreland Company.Department Direct Costs LabelSubassemblies $ 559,000 P1Final assembly 784,000 P2Marketing 294,000 P3Building occupancy 94,000 S1Research and development 129,000 S2Supervision 54,000 S3Use of services by other departments is as follows.  User DepartmentsService Cost Center Sub-assemblies Final Assembly Marketing Building Occupancy R&D SupervisionBuilding occupancy 0.30 0.25 0.20 --- 0.10 0.15R&D 0.50 0.50 --- --- --- ---Supervision 0.30 0.20 0.30 0.10 0.10 ---The equation for department P1 (subassemblies) is:Multiple ChoiceP1 = $559,000 + 0.30S1 + 0.50S2 + 0.30S3.P1 = 0.30S1 + 0.50S.P1 = $559,000 + 0.25P2 + 0.20P3 + 0.10S2 + 0.15S3.P1 = 0.30S1 + 0.50S2 + 0.30S3.

Question

The following is a system of simultaneous linear equations to allocate costs using the reciprocal method. Matrix algebra is not required.The following costs were incurred in three operating departments and three service departments in Westmoreland Company.Department Direct Costs LabelSubassemblies 559,000 P1Final assembly 784,000 P2Marketing 294,000 P3Building occupancy 94,000 S1Research and development 129,000 S2Supervision 54,000 S3Use of services by other departments is as follows.  User DepartmentsService Cost Center Sub-assemblies Final Assembly Marketing Building Occupancy R&D SupervisionBuilding occupancy 0.30 0.25 0.20 --- 0.10 0.15R&D 0.50 0.50 --- --- --- ---Supervision 0.30 0.20 0.30 0.10 0.10 ---The equation for department P1 (subassemblies) is:Multiple ChoiceP1 = 559,000 + 0.30S1 + 0.50S2 + 0.30S3.P1 = 0.30S1 + 0.50S.P1 = $559,000 + 0.25P2 + 0.20P3 + 0.10S2 + 0.15S3.P1 = 0.30S1 + 0.50S2 + 0.30S3.

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Solution

The correct equation for department P1 (subassemblies) is:

P1 = $559,000 + 0.30S1 + 0.50S2 + 0.30S3.

This equation is derived from the given information. The $559,000 is the direct cost for the subassemblies department. The other terms in the equation represent the costs allocated from the service departments to the subassemblies department. For example, 0.30S1 means that 30% of the costs from the Building Occupancy department (S1) are allocated to the subassemblies department (P1). Similarly, 0.50S2 means that 50% of the costs from the Research and Development department (S2) are allocated to the subassemblies department, and 0.30S3 means that 30% of the costs from the Supervision department (S3) are allocated to the subassemblies department.

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