Maria plans to establish a printing booth in New York City with one service window that would be open for 200 hours per month. The offered unit will cost 200 USD a month to rent for each car space. The number of car spaces that Maria should allot for her clients must be decided. Maria estimates that she will make an average profit of 4 USD each client served (zero when soft copies are dropped off and 8 USD when the printed materials are picked up), excluding the cost of renting the booth. Additionally, she predicts that customers will arrive at a mean rate of 20 per hour at random (a Poison process), yet those who find the booth full will be obligated to leave. Half of the customers who find the booth full wanted to drop off the soft copies and the other half wanted to pick up their printed materials. The half who wanted to drop off the soft copies will take their business elsewhere instead. The other half of the customers who find the booth full will not be lost because they will keep trying later until they can get in and pick up their printed materials. Maria assumes that the time required to serve a customer will have an exponential distribution with a mean of 2 minutes.

1. Find the average number of cars in the printing booth (Average number of cars in the printing booth if the car space provided is 2)
2. Find the mean rate at which customers are lost if the car space provided is 2.
3. How much time does a customer spend in the printing booth on average if the car space is 2?
4. What is the average number of customers waiting at any given time if the car space is 2?
5. How long, on average, will a customer wait before staff can attend to him/her if the car space is 2?
6. Calculate the decrease in the mean rate at which customers are lost if the car space provided is increased from 2 to 3 ?
7. Calculate the expected profit per hour (excluding space rental costs) if the car space provided is 2
8. Calculate the increase in expected profit per hour if the car space provided is increased from 2 to 3.
9. Compare the increases in expected profit with the cost per hour of renting each car space. How many car spaces should Maria provide?