Problem $3.$ Customers arrive at the theater line at the rate of $100$ per hour. The ticketseller averages $30$ seconds per customer, which includes selling the ticket and placingvalidation stamps on customers parking lot receipts. Assume that the interarrivaltimes and the service times follow exponential distribution.a$.$ What is the average time customers spend in the system?b$.$ What would be the effect on customer time in the system of having a secondticket taker doing nothing but placing validation stamps on customers parkinglot receipts, thereby cutting the average service time to $20$ seconds?c$.$ If a second window was opened with both servers doing both tasks $($sell ticketsand place validation stamps$)$ and serving a single queue line, what is theaverage customer time in the system?