Lawn Products produces two products $(x$ and $Y)$ and a by$-$product $($Z$)$ from a joint process using a raw material $($Alpha$).$ The company chooses to allocate the costs on the basis of the physical quantities method.

Last month, it processed $20,000$ pounds of Alpha at a total cost of $$96,000.$ The output of the process consisted of $33,750$ units of product $x,41,250$ units of product $Y,$ and $6,800$ units of by$-$product $Z.$ By$-$product $Z$ can be sold for $$18,060.$ This is considered to be its net realizable value, which is deducted from the processing costs of the main products.

Required:

What amount of joint costs should be assigned to each of product $x$ and product $Y?$

$\backslash$table$[[,$Joint Costs$],[$Product $x,],[$Product $Y,]]$