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			Label
Subassemblies	$	560,000		P1
Final assembly		785,000		P2
Marketing		295,000		P3
Building occupancy		95,000		S1
Research & development		130,000		S2
Supervision		55,000		S3

Use of services by other departments is as follows.

	User Departments
Service Cost Center	Sub-assemblies	Final Assembly	Marketing	Building Occupancy	R&D	Supervision
Building occupancy	0.40	0.25	0.15	---	0.10	0.10
R&D	0.50	0.50	---	---	---	---
Supervision	0.30	0.30	0.20	0.10	0.10	---

The equation for department P1 (subassemblies) is:

• P1 = $560,000 + 0.25P2 + 0.15P3 + 0.10S2 + 0.10S3.

• P1 = $560,000 + 0.40S1 + 0.50S2 + 0.30S3.

• P1 = 0.40S1 + 0.50S2 + 0.30S3.

• P1 = 0.40S1 + 0.50S.