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 $19,000$ pounds of Alpha at a total cost of

$$95,000.$ The output of the process consisted of $34,200$ units of

product $x,41,800$ units of product $Y,$ and $6,700$ units of by$-$product $Z.$

By$-$product $Z$ can be sold for $$9,400.$ 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 $Y?$