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

Subassemblies

Final assembly

Marketing

Building occupancy

Research & development

Supervision

Direct Costs Label

$ $565,000$

P$1$ P$2$ P$3$ S$2$ S$3$

$790,000$

$300,000$

$100,000$

$135,000$

$60,000$

:$43$

Use of services by other departments is as follows

$1$C

User Departments

Building

Marketing

Occupancy

$0\mathrm{.}20$

Sub$-$

assemblies

$0\mathrm{.}30$

$0\mathrm{.}50$

$0\mathrm{.}30$

Final

Assemb ly

$0\mathrm{.}25$

$0\mathrm{.}50$

$0\mathrm{.}30$

Service Cost Center

Building occupancy

R&D

Supervision

R&D

$0\mathrm{.}10$

Supervision

$0\mathrm{.}15$

$0\mathrm{.}20$

$0\mathrm{.}10$

$0\mathrm{.}10$

The equation for department S$1($building occupancy$)$ is: