Hargrove Hospital is experiencing cutbacks in funding and revenues. One suggestion for saving money is to eliminate one of its two birthing stations. The hospital estimates that this cut will save $25,000 per year in direct expenses. The hospital is also considering adding additional birthing stations at an annual cost of $30,000 per station because when all birthing stations are occupied, women in labor are sent to one of the hospital’s surgery rooms. The estimated cost per hour for the use of a surgery room for maternity purposes is $400 (due to the need to reschedule surgeries). Hence, the expense of additional birthing stations may be more than offset by the savings from a decreased use of the hospital’s surgery rooms. Studies have indicated that an average of six women a day go into labor at the hospital and that the average time spent in a birthing station is two hours. Women who need a birthing station arrive at the hospital according to a Poisson process.
1. Determine the optimum number of birthing stations (the number to maximize the hospital's yearly savings compared to the current situation).
2. Compared to the current situation, how much will be saved per year by using the optimum number of birthing stations?