Janson\'s Department Store in Stark, Ohio, maintains a successful catalog sales

Question

Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 12 per hour. The clerk can take an order in an averge of 4.0 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential.

The Cost of the clerk is $10 per hour, but because of lost goodwill and sales, Janson's loses about $30 per hour of customer time spent waiting for the clerk to take an order.

(part A and B is already done)

a.) The average time that catalog customers must wait before their calls are transferred to the order clerk= 16 minutes

b.) The average number of callers waiting to place an order= 3.2 callers

(NEEDS ANSWERING BELOW)

The present total cost per hour (service cost+waiting cost)= $___ per hour (round response to two decimal places)

c.) Janson's is considering adding a second clerk to make calls. The stores cost would be the same $12 per hour. The total cost (service cost + waiting cost) = $___ per hour (round your response to two decimal places)

By hiring the second clerk, the total cost savings per hour for Jansons's = $____ per hour (round your response to two decimal places)

Explanation / Answer

Arrival rate (lambda) = 12 calls per hour

Service rate (mu) = 60/4 = 15 calls per hour

Average waiting time = lambda/mu*(mu-lambda) = 0.266=16 minutes

Average no. of caller waiting to place an order= lambda^2/mu*(mu-lambda)= 3.2 caller

Average no. of caller waiting in system= lambda/(mu-lambda)= 4

Present total cost per hour = service cost + waiting cost = 3*10 + 4*30 = $150

c) Average rate of utilization = lambda/2*mu=0.4

Probability of no customer in system = 0.37

Avg. no. of caller in system= 0.93 caller

Avg. no. of caller waiting = 0.93-(12/15) = 0.13 caller

Waiting cost = $27.9

Service cost = $20

Total cost = $47.9

Total cost saving per hour = 150-47.9 = $102.1

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