Weston Products manufactures an industrial cleaning compound that goes through three processing departments$$Grinding$,$ Mixing, and Cooking. All raw materials are introduced at the start of work in the Grinding Department. The Work in Process T$-$account for the Grinding Department for May is given below:

Work in Process$$Grinding Department

Debit Credit

Inventory, May $121,800$ Completed and transferred to the Mixing Department $?$

Materials $133,400$

Conversion $225,500$

Inventory, May $31?$

The May $1$ work in process inventory consisted of $18,000$ pounds with $$14,600$ in materials cost and $$7,200$ in conversion cost. The May $1$ work in process inventory was $100\%$ complete with respect to materials and $30\%$ complete with respect to conversion. During May, $167,000$ pounds were started into production. The May $31$ inventory consisted of $15,000$ pounds that were $100\%$ complete with respect to materials and $60\%$ complete with respect to conversion. The company uses the weighted$-$average method in its process costing system.

Required:

$1.$ Compute the Grinding Department's equivalent units of production for materials and conversion in May.

$2.$ Compute the Grinding Department's costs per equivalent unit for materials and conversion for May.

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

$4.$ Compute the Grinding Department's cost of units transferred out to the Mixing Department for materials, conversion, and in total for May.