Builder Products, Incorporated, uses the weighted$-$average method of process costing. It manufactures a caulking compound that goes through three processing stages prior to completion. Information on work in the first department, Cooking, is given below for May:

Production data:

Pounds in process, May $1$; materials $100\%$ complete; conversion $90\%$ complete $70,000$

Pounds started into production during May $350,000$

Pounds completed and transferred out $?$question mark

Pounds in process, May $31$; materials $70\%$ complete; conversion $30\%$ complete $30,000$

Cost data:

Work in process inventory, May $1$:

Materials cost $ $86,900$

Conversion cost $ $39,300$

Cost added during May:

Materials cost $ $451,510$

Conversion cost $ $216,060$

Required:

For May:

Compute the equivalent units of production for materials and conversion.

Compute the cost per equivalent unit for materials and conversion.

Compute the cost of ending work in process inventory for materials, conversion, and in total.

Compute the cost of units transferred out to the next department for materials, conversion, and in total.

Prepare a cost reconciliation report.