A company is going to hire a repairman to look after four identical unreliable machines. The machines break down randomly according to a Poisson process of mean rate of 3 per day.
The non-productive time of any machine costs the firm 200 dollars per day. The firm can hire a slow, cheap repairman charging 500 dollars per day who repairs at an average rate of 4 machines per day.
Alternatively the firm can hire a fast, experienced repairman charging 1; 000 dollars per day who repairs at an average rate of 5 machines per day.
In either case repair time is assumed to be exponentially distributed. Compute the expected running costs in both cases and determine which repairman should be hired.