Helix Corporation uses the weighted$-$average method in its process costing system. It produces prefabricated flooring in a series of steps carried out in production departments. All of the material that is used in the first production department is added at the beginning of processing in that department. Data for May for the first production department follow:

Units Percent Complete

Materials Conversion

Work in process inventory, May $178,000100\%50\%$

Work in process inventory, May $3158,000100\%30\%$

Materials cost in work in process inventory, May $1$ $ $61,200$

Conversion cost in work in process inventory, May $1$ $ $18,100$

Units started into production $253,200$

Units transferred to the next production department $273,200$

Materials cost added during May $ $137,520$

Conversion cost added during May $ $260,876$

Required:

$1.$ Calculate the first production department's equivalent units of production for materials and conversion for May.

$2.$ Compute the first production department's cost per equivalent unit for materials and conversion for May.

$3.$ Compute the first production department's cost of ending work in process inventory for materials, conversion, and in total for May.

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