Question 1At a bank’s customer service hotline, telephone calls come in at the rate of 57 per hour.  The average time that a customer service officer needs to handle a customer’s request is 3 minutes.  After handling a call, the customer service officer spends an average of one minute writing up the call conversation summary.  There are 5 officers on duty at each shift.Question 1(a) What is the arrival rate ?, the service rate µ, and the number of servers? What does the M/M/s queueing model predict for the average queue length, and the average waiting time?Question 1(b) The management at the bank is now considering hiring one less officer at each shift in order to reduce the labor cost.  In this scenario, what does the M/M/s queueing model predict for the average queue length, and the average waiting time?Question 2Man Lok owns a flower stand at the South Horizon MTR station.  He buys flowers from a wholesaler at $5 per flower and sells them for $10 per flower.  Based on last year’s sales data, he has found that the daily demand can be approximated by a normal distribution with a mean of 100 and a standard deviation of 20.  When he ends the day with more flowers than customers, he can sell all leftovers for $2 per flower.  Note: to make the grading easier, use four decimal places for the critical fractile/ratio.Question 2(a) What is the underage cost, the overage cost, the critical ratio, and the optimal order quantity?Question 2(b) When he has more demand than flowers in store, he estimates that there is some lost goodwill of $20 per flower (including the opportunity cost of lost sales).  What is the underage cost, the overage cost, the critical ratio, and the optimal order quantity?Question 3An airline serving Hong Kong International Airport is considering overbooking its flights to avoid flying with empty seats.  For example, the ticket agent is thinking of taking seven reservations for an airplane that has only six seats.  During the past month, the no-show experience has beenNo-shows01234Percentage3025201510The operating costs associated with each flight are pilot, $150; first officer, $100; fuel, $30; and landing fee, $20.A one-way ticket sells for $80 and the cost of not honouring a reservation is a free lift ticket worth $50 plus a seat on the next flight.Question 3(a) Construct a payoff matrix to determine recommended overbooking strategy.  What is the expected profit per flight for your overbooking choice?Question 3(b) What are the underage cost and overage cost?  Explain their meanings.Question 3(c) What is the critical ratio, and what would be your recommendation for overbooking?I need the detailed solutions of these questions