1. The Lower Colorado River Authority (LCRA) has been studying congestion at the boat-launching ramp near Mansfield Dam. On weekends, the arrival rate averages five boaters per hour, Poisson distributed. The average time to launch or retrieve a boat is 10 minutes, with negative exponential distribution. Assume that only one boat can be launched or retrieved at a time.

Question a: The LCRA plans to add another ramp when the average turnaround time (i.e., time in the system) exceeds 90 minutes. Therefore, the LCRA should begin to consider adding another ramp when the average arrival rate is _______ per hour. (Hint: please provide your answer with the precision of two digits after the decimal point, e.g., 1.23)

Question b: If there were room to park only two boats at the top of the ramp in preparation for launching, then the probability of an arrival finding insufficient parking space will be________ . (Hint: please provide your answer with the precision of two digits after the decimal point, e.g., 1.23)

2. Customers arrive at Mike & Steves bookstore according to a Poisson process at a mean rate of 48 per hour. The store pays its sales clerks $7.50 per hour in wages and benefits. Mike and Steves estimates the goodwill cost of a customer waiting to be served at $6.00 per hour and the goodwill cost of a customer being served at only $1.00 per hour. Customer service time follow an exponential distribution and average 2 minutes.

Question a: To minimize the stores total average hourly costs, Mike & Steves should employ_______ sales clerk(s). (Hint: please fill the blank with a positive integer, e.g., 1, 2, 3, 4, 5, 6, ...)

Question b: If the customer arrival rate increases by 50% and the goodwill cost of a customer waiting to be served and being served were doubled, then Mike & Steves should employ ________ sales clerk(s) to minimize the stores total average hourly costs. (Hint: please fill the blank with a positive integer, e.g., 1, 2, 3, 4, 5, 6, ...)