$12.$ Valamoto Co$.$ manufactures a single product that goes through two processes $$ mixing and cooking. The following data pertains to the Mixing Department for September $2007.$

Work$-$in$-$process inventory, September $138,000$ units

Conversion $60\%$ completed

Work$-$in$-$process inventory, September $3024,000$ units

Conversion $40\%$ completed

Units started into production $86,000$ units

Units completed and transferred out $?$ units

Costs:

Work$-$in$-$process inventory, September $1$

Material R $$104,600$

Material S $135,920$

Conversion $184,996$

Costs added during September:

Material R $233,920$

Material S $215,000$

Conversion $474,796$

Material R is added at the beginning of work in the Mixing Department. Material S is also added in the Mixing Department, but not until units of product are thirty percent completed with regard to conversion. Conversion costs are incurred uniformly during the process.

Required:

$(1)$ Calculate the equivalent units for Material R using the weighted$-$average method.

$(2).$ Calculate the equivalent units for Material S using the weighted$-$average method.

$(3)$ Calculate the equivalent units for conversion using the weighted$-$average method.

$(4)$ Calculate the unit costs using the weighted$-$average method.

$(5)$ Calculate the cost of units completed and transferred out using the weighted$-$average method.

$(6)$ Calculate the cost of ending work in process using the weighted$-$average method.