$3.$ Anderson Chemicals produces a chemical and uses process costing. There are three processing departments$$Mixing$,$ Refining, and Packaging. On January $1,$ the Refining Department had $15,000$ gallons of partially processed product in production. During January, $36,000$ gallons were transferred in from the Mixing Department, and $30,000$ gallons were completed and transferred out. At the end of the month, $21,000$ gallons of partially processed product remained in the Refining Department. See additional details below.

Refining Department, ending balance at January $31$

Percent completed for materials cost: $65\%$

Percent completed for conversion cost: $80\%$

Costs associated with refining Direct Materials $$90,000,$ Direct Labor $$75,000,$ and Overhead $$125,000.$

a$.$ Complete the $4$ step process to assign costs to equivalent units.