A company’s machines break down according to a Poisson process at a mean rate of 3 per hour. Nonproductive time on any machine costs the company $60 per hour. The company employs a maintenance person who repairs machines at a mean rate of μ machines per hour (when continuously busy) if the company pays that person a wage of $5μ per hour. The repair time has an exponential distribution.
Determine the hourly wage that minimizes the company’s total expected cost.