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Vacations Inc. (VI) markets time-share condominiums throughout North America. One way the company

 

generates sales leads is by offering a chance to win a free mini-vacation to anyone who fills out an

 

information card at places it in VI boxes located in malls. The ones who fill out the form and indicate an

 

adequate income level receive a letter from VI with a toll-free number. A call to the toll-free number

 

reveals that the mini-vacation consists of a free dinner, entertainment, and two-night stay at one of VI?s

 

time-share properties. About half the people who call to claim their ?prize? reject the offer once they find out about the twohour property tour. About 40% accept the mini-vacation and do the tour, but do not buy anything. The

 

remaining 10% accept the offer, accept the mini-vacation and ultimately purchase a time-share. Each

 

mini-vacation costs VI about $250 and generates a net profit of $7,000. VI?s call center operates from 10 am to 10 pm daily with three sales representatives and receives calls at

 

the rate of 50 per hour, with inter-arrival times being exponentially distributed. It takes an average of 4

 

minutes to handle each call with actual times being exponentially distributed. The phone system keeps

 

up to 10 callers on hold. Assume those who receive a busy signal do not call back. Use waiting line analysis to answer the following questions. (1) On average, how long are customers on hold before they get to speak to a sales person? (2) If VI has a service goal of less than 3 minutes for average waiting time, how many salespeople

 

should it employ?

 

(3) Would the capacity have to be altered for a service goal of 1 min or less of average wait time? (4) What is the expected value of each call to VI? (5) On average, how many customers does each salesperson process in a single day? (Hint: Look at the

 

utilization of servers)

 

(6) What is the daily expected profit? (7) Suppose VI pays its sales people $12 per hour. How many sales people should it employ to

 

maximize daily profit?

 

(8) If the customer call arrival rate increased to 60 calls per hour, how would it affect your decision on

 

the number of sales

 

people?

 







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