Solex Company manufictures $3$ products from a common input in a joint processing operation. Joint processing costs up to the split$-$off point total $$100,000$ per year. The company allocates these costs to the joint products on the basis of their total sales value at the split$-$off point. These sales values are as follows: product X: $$50,000$; product Y: $$90,000$; and product Z: $$60,000.$

Ench product may be sold at the split$-$off point or processed further. Additional processing requires no specinl facilities. The additional processing costs and the sales value after further processing for each product $($on an annual basis$)$ are shown below:

$\backslash$table$[[$Product$,\backslash$table$[[$Additional$],[$Processing$],[$Costs$]],\backslash$table$[[$Sales Value$],[$after Further$],[$Processing$]]],[$X$,35,000,80,000],[$Y$,40,000,150,000],[$Z$,12,000,75,000]]$

Which product $($s$)$ should be sold at the split$-$off point and which product $($s$)$ should be processed further? Show computations.

$\backslash$table$[[,$Product $x,$Product $Y,$Product $Z$