A machine begins in good running condition, lasts for an exponential length of time with rate \(\lambda_{1}\), then breaks down. The repair of the machine lasts for an exponential period of time with rate \(\lambda_{2}\), after which the machine is completely repaired, lasts for another exponential length of time with rate \(\lambda_{1}\), is repaired again, etc. If a repair costs \(c\) dollars, find the long-run cost of repairs per unit time.