You manage the Big-Rig Service Center, which runs a thriving business performing repairs on large trucks.  The number of trucks arriving at the facility in need of repair each morning is well-modeled by a Poisson random variable with a mean value of 3.8.  If you have a free service bay available for an arriving truck, you start servicing it immediately.  Trucks that you cannot immediately accommodate with a free service bay do not wait, but go to a competitor’s facility instead.  You currently have 5 service bays, but since you frequently have to turn away business, you are considering expanding to 6, 7, or possibly 8 bays.

Including debt service, insurance, and taxes, your costs for these expansion options, converted to a daily payment, would be:

Repairing each truck can take either 1, 2, or 3 full days; and you cannot tell in advance how long the work will take.  There is a 30% chance that a truck can be completed by the end of one day, in which case you charge $800.  Given that service cannot be completed the first day, there is 75% chance it will be finished at the end of the next day, in which case your total charge is $1,500.  Otherwise, completing the service takes three full days or work, for which you charge $2,100.  Your operating costs are $425 per occupied service bay per day.