Chemical Corporation produces liquid chemicals A and B from a joint process. Joint costs are allocated on the basis of relative sales value at split$-$off. It costs $$4,560$ to process $500$ gallons of Product A and $1,000$ gallons of Product B to the split$-$off point. The market value at split$-$off is $$10$ per gallon for Product A and $$14$ for Product $B.$ Product $B$ requires an additional process beyond split$-$off at a cost of $$2$ per gallon before it can be sold. What is Chemical's cost to produce $1,000$ gallons of Product B$?$

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$$4,860$

$$5,360$

$$3,360$

$$5,040$