Robinson Products Company has two service departments $($S$1$ and S$2)$ and two production departments $($P$1$ and P$2).$ The distribution of each service department$$s efforts $($in percentages$)$ to the other departments is:

From To

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

S$1-20\%30\%?$

S$2-20\%?40$

The direct operating costs of the departments $($including both variable and fixed costs$)$ are:

S$1$ $ $175,000$

S$265,000$

P$152,000$

P$2130,000$

Determine the total cost of P$1$ and P$2$ using the reciprocal method.