Cordner Corporation has two production departments, P$1$ and P$2,$ and two service departments, S$1$ and S$2.$ Direct costs for each department and the proportion of service costs used by the various departments for the month of July are as follows:

Proportion of Services Used by:

Department Direct costs S$1$ S$2$ P$1$ P$2$

S$1$ $ $150,0000\mathrm{.}700\mathrm{.}100\mathrm{.}20$

S$2$ $ $182,0000\mathrm{.}200\mathrm{.}300\mathrm{.}50$

P$1$ $ $226,000$

P$2$ $ $142,000$

Under the step method of allocation, the total amount of service costs allocated to producing departments would be: