Wexpro, Incorporated, produces several products from processing $1$ ton of clypton, a rare mineral. Material and processing costs total $$78,000$ per ton, one$-$fourth of which is allocated to product X$15.$ Eight thousand four hundred units of product X$15$ are produced from each ton of clypton. The units can either be sold at the split$-$off point for $$10$ each, or processed further at a total cost of $$6,000$ and then sold for $$13$ each.

Required:

$1.$ What is the financial advantage $($disadvantage$)$ of further processing product X$15?$

$2.$ Should product X$15$ be processed further or sold at the split$-$off point?