Builder Products, Incorporated, uses the weighted$-$average method in its process costing system. 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 $69,000$

Pounds started into production during May $340,000$

Pounds completed and transferred out $?$

Pounds in process, May $31$; materials $80\%$ complete; conversion $20\%$ complete $15,000$

Cost data:

Work in process inventory, May $1$:

Materials cost $ $78,000$

Conversion cost $ $15,300$

Cost added during May:

Materials cost $ $405,140$

Conversion cost $ $83,950$

Required:

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

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

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

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

$5.$ Prepare a cost reconciliation report for May.