Question 3(a):
When customers arrive at Cool's Ice Cream Shop, they take a numberand wait to be called to purchase ice cream from one of the counterservers. From experience in past summers, the store's staff knowsthat customers arrive at a rate of 150 per hour on summer daysbetween 3:00 p.m. and 10:00 p.m., and a server can serve 1 customerin 1 minute on average. Cool's wants to make sure that customerswait no longer than 10 minutes for service. Cool's is contemplatingkeeping three servers behind the ice cream counter during the peaksummer hours.
(i) Will this number be adequate to meet the waiting timepolicy?
(ii) What will be the probability that 3 to 4 customers inShop?
(iii) In winter season, arrival rate of customer is reduced to halffrom 3:00 p.m. and 10:00 p.m. What decision should be taken by theowner according to cost cutting point of view?
Question 3(b):
Analysis of arrivals at a PSO gas station with a single pump(filler) has shown the time between arrivals with a mean of 10minutes. Service times were observed with a mean time of 6minutes.
(i) What is the probability that a car will have to wait?
(ii) What is the mean number of customers at the station?
(iii) What is the mean number of customers waiting to beserved?
(iv) PSO is willing to install a second pump when convinced that anarrival would expect to wait at least twelve minutes for the gas.By how much the flow of arrivals is increased in order to justify asecond booth?