Question: The number of missing items in a certain location, call it \(X\), is a Poisson random variable with mean \(\lambda\). When searching the location, each item will independently be found after an exponentially distributed time with rate \(\mu\). A reward R is received for each item found, and a searching cost of \(C\) per unit of search is incurred. Suppose that you search for a fixed time \(t\) and then stop.

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