Customers arrive to check in at the exclusive and expensive Regency Hotel’s lobby at a rate of 40 per hour (Poisson distributed). The hotel normally has three clerks available at the desk to check in guests. The average time for a clerk to check in a guest is 4 minutes (exponentially distributed). Clerks at the Regency are paid $24 per hour, and the hotel assigns a goodwill cost of $2 per minute for the time a guest must wait in line. Determine whether the present check-in system is cost-effective. If it is not, recommend what hotel management should do.
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