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Harry's Car Wash and Ashley's Department Store

Question # 00008282
Subject: Mathematics
Due on: 02/11/2014
Posted On: 02/11/2014 06:51 AM

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From historical data, Harry's Car Wash estimates that dirty cars arrive at the rate of 10 per hour all day Saturday. With a crew working the wash line, Harry figures that cars can be cleaned at the rate of one every 5 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the
A.) average number of cars in line
B.) average time a car waits before it is washed
C.) average time a car spends in the service system
D.) utilization rate of the car wash
E.) probability that no cars are in the system

Given, Arrival rate = ? = 10 cars per hour
Service rate = ? = 1 car per 5 minutes = cars per hour

Ashley's Department Store in Kansas City maintains a successful catalog sales department in which a clerk takes 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 that has waited the longest is transferred and answered first. Calls come in at a rate of about 12 per hour. The clerk is capable of taking an order in an average of 4 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. The clerk is paid $10 per hour, but because of lost goodwill and sales, Ashley's loses $50 per hour of customer time spent waiting for the clerk to take an order.
A.) What is the average time that catalog customers must wait before their calls are transferred to the order clerk?
B.) What is the average number of callers waiting to place an order?
C.) Ashley's is considering adding a second clerk to take calls. The store would pay that person the same $10 per hour. Should it hire another clerk? Explain

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Harry's Car Wash and Ashley's Department Store

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Posted On: 02/11/2014 06:53 AM
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Harry_and_Ashley_Solution.doc (75.5 KB)
Preview: XS100 xxxxxx 10 xxxx 267)(50) 10 xxx 2 170 xxxxxxx To xxxxxxxxx xxxxx cost xxxxx an additional xxxxx EMBED Equation xxxxx ART xxxxxxxxxxxxx xxx W53 xxxxx H32 056pt xxxxx YS100/ or xxxxx Equation xxxxx xxx FILE14_16eq12 xxx W67 5pt xxx 036pt XS100 xxxxxxxxx FILE14_16eq13 xxx xxx 001pt xxx 036pt XS100 xxxxxx EMBED Equation xxxxx ART xxxxxxxxxxxxx xxx W98 xxxxx H40 819pt xxxxx YS100/ Then xxxxx Equation xxxxx xxx FILE14_16eq15 xxx W122 591pt xxx 779pt XS100 xxxxxx The xxxx xx having xxx clerks would xx Ct/hour service xxxx waiting xxxx xxxxx Equation xxxxx ART FILE14_16eq18 xxx W159 939pt xxx 252pt xxxxx xxxxxx 20 xxxx 0127)(50) 20 x 62 27 xxxxxxx The xxxxxxxxxxxx xxxx that xx the firm xxxxx a second xxxxx they xxxxx xxxxxxxx end xx saving 170 xx 27 62 xxx 5/hour xx xxxxx it xx a wise xxxx to hire xxx second xxxxx xxxxxxxxxxxxxxxxxx 77uFV xxx JXIFCkqju1 n1 x edGWZOG4Fr,bMl5_-kBI2NqJl/03, yh2 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx mmFX).....
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