$18-35.$ EQUIVALENT UNITS, COMPREHENSIVE. Imperial Bakery supplies cupcakes to a national grocery chain for their private label. The cupcakes must meet specific requirements of the grocery chain. Imperial uses a specific process to produce the cupcakes to the grocery chain$$s specifications.

The cupcakes are baked, filled and frosted, in that sequence. Materials are added as follows:

The basic ingredients for the cupcakes are added at the start of the baking process.

The filling is inserted into the cupcakes when cupcakes are $90\%$ complete.

The frosting is added at the end of the process.

Of the total conversion costs, $70\%$ are incurred during the baking process when cupcakes are $80\%$ complete, an additional $10\%$ are incurred at the start of the filling process when the cupcakes are $90\%$ complete, and the remaining $20\%$ are incurred when the frosting is done at the end of the process.

On May $1,2020,$ Imperial had $500$ dozen cupcakes in inventory. These cupcakes were $90\%$ complete and ready for filling and frosting. During May, $1,500$ dozen cupcakes were put into production. At the end of May, Imperial had $200$ dozen cupcakes that had been baked and filled and ready for frosting.

Required

Using the weighted$-$average method of process costing, compute equivalent units of work done for $($a$)$ baking materials, $($b$)$ filling materials, $($c$)$ frosting materials, and $($d$)$ conversion costs for the month of May.

Using the FIFO method of process costing, compute equivalent units of work done for $($a$)$