Vaughn's woodworking business produces two products from its joint process: one main product $($sanded and finished trim pieces$)$ and one by$-$product $($sawdust$/$shavings$).$ The joint process has a cost of $$31,000,$ which results in trim pieces worth $$53,000$ and sawdust$/$shavings that can be sold for $$2,900.$ If Vaughn uses the production method to account for by$-$products, determine how much of the joint process cost will be allocated to each product. In other words, how much inventory cost will be recorded for each product?