Murteza is an entrepreneur and plans to open PIRILDAK CAR WASH company at a shopping mall's parking area. Murteza thinks about a car washing facility with 1 server. Washing bay requires 3 parking lots and he needs parking lots for waiting customer cars, too. Each lot's rent is 1000 TL / year. 5 customers/hr. arrive to PIRILDAK CAR WASH and it takes 10 min. to wash a car. Price for washing service is 20 TL/car. Shopping time for a customer is 30 min. (service time and interarrival times are exponentially distributed). When average time to wash a car exceeds this time, Murteza assumes a waiting cost of 10 TL/hr for each customer. Murteza also considers lost customer as cost 

a) Considering renting lots for waiting cars between 0 and 10, make a queue analysis that gives the expected profit for Murteza. 

b) Shopping mall offers Murteza "pay rent for Z lots, use all parking lots". Comparing M/M/1/GD/ ∞ / ∞ solution (where rent is defined w.r.t. Z lots) with best M / M / 1 / GD / С/ ∞ solution, calculate Z for Murteza. Comment on Z.