Staff size maximising expected birthday holiday hours

A company closes for the whole day on any date that is the birthday of at least one of its employees; on every other date all employees work $24$ hours. Birthdays are independent and uniform over $365$ days. The company wants to choose its head count $n$ to maximise the expected total number of employee-hours not worked in a year. What $n$ should it pick? Answer $-1$ if no finite $n$ is optimal.

$-1$ (no finite optimum). The expected number of closed days is $365\left(1-(364/365)^n\right)$, which increases with $n$. Total hours off are $24n$ times that, a product of two increasing positive factors, so it grows without bound and more staff is always better.