Material $P$ is added at the beginning of work in the Mixing Department. Material $Q$ is also added in the Mixing Department, but not until units of product are forty percent completed with regard to conversion. Conversion costs are incurred uniformly during the process.

Required: Use weighted$-$average method to calculate:

$($a$)$ Equivalent units for Material P$,$ Material Q and conversion, respectively.

$($b$)$ Cost per equivalent unit, $($keep two decimal digits$).$

$($c$)$ Costs of units transferred out.