30. The customers in the Raja Ji Departmental Store, which is being renovated, order their requirements in the different sections, pay cash at the cash counters and then, finally, obtain delivery from the 'delivery counter'. After taking delivery, the customers queue up to leave through a checkout lane.

The manager is in a fix whether to provide 2 checkout lanes or 3. He needs your help and provides you with the following information.

"It is estimated that the mean arrival of the customers at the checkout would be 7 per one-minute period and the service rate would be 4 customers per one-minute period per lane. Further, due to goodwill, customers' waiting time costs the store 10 p per minute. The cost to operate a lane is Rs 2.65 per hour."

For Your analysis, assume that (i) customers form a single queue, and (ii) the arrival and service rates are Poisson distributed.

(a) Show to the manager the comparative values of P(0), L8 , Wq and Ws for 2 and 3 lanes, respectively.

(b) Suggest to the manager whether to provide 2 lanes or 3.