Series System Replacement Costs via Competing Exponentials

A machine has two critical components in series: component A with lifetime $\operatorname{Exp}(3)$ and component B with lifetime $\operatorname{Exp}(5)$, independent of each other. When either fails, the entire machine stops, the failed component is replaced (cost $\$20$ for A, $\$50$ for B), and both components restart fresh (the survivor restarts by memorylessness, the replacement is new). Find the expected replacement cost per unit time in the long run.