The Tanya-Arun-Suja-Umang-Anish-Shrish (TASUAS) team at the Taj Hotel in Mumbai, is well versed in Waiting Line theory and Quant Methods and can serve drinks at the rate of one every 50 seconds. During a hot evening in April, the bar was particularly busy and every 55 seconds someone was at the bar asking for a drink. (4+4+4+4+4 = 20 pts)

a) Assuming that everyone in the bar drank at the same rate and that people were served on a first-come, first served basis, how long would you expect to have to wait for a drink?

b) How many people would you expect to be waiting for drinks?

c) How busy is the bartender (what is the utilization rate)?

d) If the bartender is replaced with an automatic drink dispensing machine, how long would you expect to have to wait for a drink?

e) If the bartender is replaced with an automatic drink dispensing machine, how many people would you expect to be waiting for drinks

a) Machine A

b) Machine B

c) Machine C

d) You would be indifferent between machines A and C

e) You would be indifferent between machines A and B d) As an added convenience to customers, the Aditya-Nayan-Sreenidhi-Deep-Christina (ANSDC) Meds, a new health care provider has added a drive-up window for allergy and flu shots as well as automated serum retrieval for its regular drive-up customers. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 50 seconds. The automated retrieval system requires 45 seconds to locate and prepare a shot using a customers specialized serum. To help determine the amount of space needed for the line at the drive-up at new franchises, ANSDC Meds would like to know the following information: (4+4+4 = 12 pts)

i) The expected average time in the system

ii) The average line length (in cars)

iii) The average number of cars in the system (both in line and at the window