Sonimad Sawmill Incorporated $($SSI$)$ purchases logs from independent timber contractors and processes the logs into the following three types of lumber products:

Studs for residential building $($walls$,$ ceilings$).$

Decorative pieces $($fireplace mantels, beams for cathedral ceilings$).$

Posts used as support braces $($mine support braces, braces for exterior fences around ranch properties$).$

These products are the result of a joint sawmill process that involves removal of bark from the logs$,$ cutting the logs into a workable size $($ranging from $8$ to $16$ feet in length$),$ and then cutting the individual products from the logs$,$ depending on the type of wood $($pine$,$ oak, walnut, or maple$)$ and the size $($diameter$)$ of the log$.$ The joint process results in the following costs and output of products for a typical month.

$\backslash$table$[[$Joint production costs:,$],[$Materials $($rough timber logs$),500,000],[$Debarking $($labor and overhead$),50,000],[$Sizing $($labor and overhead$),200,000],[$Product cutting $($labor and overhead$),250,000],[$Total joint costs,$$1,000,000$