Autry Company manufactures veterinary products. One joint process involves refining a chemical $($dactylyte$)$ into two chemicals $-$ dac and tyl$.$ One batch of $5,000$ gallons of dactylyte can be converted to $2,000$ gallons of dac and $3,000$ gallons of tyl at a total joint processing cost of $$12,000.$ At the split$-$off point, dac can be sold for $$3$ per gallon and tyl can be sold for $$4$ per gallon. Autry has just learned of a new process to convert dac into prodac. The new process costs $$4,000$ and yields $1,700$ gallons of prodac for every $2,000$ gallons of dac. Prodac sells for $$5$ per gallon.

Refer to Figure $13-6.$ What is Autry's profit from refining one batch of dactylyte if both dac and tyl are sold at the split$-$off point?

$$6,000$

$$12,000$

$$7,000$

$$18,000$

$$15,000$