Arkansas Corporation manufactures liquid chemicals A and $B$ from a joint process. It allocates joint costs on the basis of sales value at split$-$off. Processing $4,700$ gallons of product A and $1,600$ gallons of product $B$ to the split$-$off point costs $$5,600.$ The sales value at split$-$off is $$2\mathrm{.}00$ per gallon for product A and $$23\mathrm{.}50$ per gallon for product $B.$ Product $B$ requires additional separable processing beyond the split$-$off point at a cost of $$2\mathrm{.}20$ per gallon before it can be sold at a price of $$34$ per gallon.

Required:

What is the company's cost to produce $1,600$ gallons of product $B?$

Product cost