Kim Airedale, a manager of Waggers, Inc., was reviewing the water bills of a dog daycare and spa. She determined that its highest and lowest bills of $$3,400$ and and November, respectively. If $600$ dogs were washed in May and $100$ dogs were washed in November, what was the variable cost per dog associated with the co nearest cent.$)$

A$.$ $$0\mathrm{.}80$

B$.$ $$5\mathrm{.}67$

C$.$ $$30\mathrm{.}00$

D$.$ $$4\mathrm{.}29$