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 $568,000 P1 Final assembly 793,000 P2 Marketing 303,000 P3 Building occupancy 103,000 $1 Research & development 138,000 82 Supervision 63,000 83 Use of services by other departments is as follows. 4 User Departments Sub- Final Service Cost Center assemblies Building occupancy Assembly 0.30 0.25 Marketing 0.20 Building Occupancy R&D 0.15 Supervision 0.10 R&D 0.50 0.50 --- --- www Supervision 0.20 0.30 0.20 0.20 0.10 The equation for department S2 (research and development) is: