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 $71,000$

Pounds started into production during May $360,000$

Pounds completed and transferred out $?$question mark

Pounds in process, May $31$; materials $75\%$ complete; conversion $25\%$ complete $31,000$

Cost data:

Work in process inventory, May $1$:

Materials cost $ $90,100$

Conversion cost $ $46,400$

Cost added during May:

Materials cost $ $468,590$

Conversion cost $ $255,335$

Required:

For May:

$1.$ compute the equivalent units of production for materials and conversion.

$2.$ Compute the cost per equivalent unit for materials and conversion.

$3.$ Compute the cost of ending work in process inventory for materials, conversion, and in total.

$4.$ Compute the cost of units transferred out to the next department for materials, conversion, and in total.

$5.$ Prepare a cost reconciliation report.