The auxiliary bookstore in the room has one checkout counter where one employee operates the cash register. People arrive at a rate of 24 per hour following a Poisson distribution and service times are exponentially distributed, with a mean rate of 30 customers per hour. The average purchase per customer is $48.

The bookstore considers adding another employee to assist the present operator. There are several options to utilize this additional staff. One is to enable more customers to be served in less time, thus increasing the service rate from 30 customers per hour to 40 customers per hour. Alternatively, the bookstore could redesign to add a second cash register, one has its own line. Assume existing customers split evenly between the two cash registers and each has her/his own line, just like most grocery stores. Finally, the bookstore can use this additional staff as a second register but unlike option 2, there is only one combined line shared by these two registers (like most of the bank tellers).

Assume the hourly rate for each employee is $20, regardless what job do they perform. Assume that each customer is only waiting for up to 1 minute to be served, or would renege (i.e., leave the store unpurchased). Which option should the bookstore adopt to minimize the total cost?

Answer the above questions by filling in the table below. Points for each column are shown below. You MUST show your calculations/steps at least for P₀ to get full credits. For the steps, you can handwrite

Impact	Original (demonstrated in class)	(option 1) Increase service rate (1pt) λ = µ = S=	(option 2) Reduce arrival rate (1.5pt) λ = µ = S=	(option 3) Become a second server (2pt) λ = µ = S=
Time spent on waiting (Wq)	8min
No. of customer in system (L)	4
P0	0.2
Total cost	20*1+4*48=212