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Use the Random number table provided (Table 4) for #s 1 & 2 Problems The problems that follow involve simulations that are to be done by hand. You are aware that to obtain accurate and mean- ingful results, long periods must be simulated. This is usually handled by computer. If you are able to program some of the problems using a spreadsheet or QM for Windows, we suggest that you try to do so. If not, the hand simulations will still help you in understanding the simulation process. 1. Clark Property Management is responsible for the maintenance, rental, and day-to-day operation of a large apartment complex on the east side of New Orleans George Clark is especially concerned about the cost projections for replacing air conditioner compres- sors. He would like to simulate the number of com- pressor failures each year over the next 20 years. Using data from a similar apartment building he manages in a New Orleans suburb, Clark establishes the following table of relative frequency of failures during year: NUMBER OF A.C. PROBABILITY COMPRESSOR FAILURES (RELATIVE FREQUENCY) 0.06 1 0.13 2 0.25 3 0.28 4 0.20 5 0.07 6 0.01 He decides to simulate the 0-year period by select- ing two-digit random numbers from the third col- umn of Table 4. starting with the random number 50. Conduct the simulation for Clark. Is it common to have three or more consecutive years of operation with two or fewer compressor failures per year? 2. The number of cars arriving per hour at Lundberg's Car Wash during the past 200 hours of operation is observed to be the following: NUMBER OF CARS ARRIVING FREQUENCY 3 fewer 4 20 5 30 6 50 7 60 8 40 9 more Total 200 (a) Set up probability and cumulative probability distribution for the variable of car arrivals. (b) Establish random number intervals for the variable. (c) Simulate 15 hours of car arrivals and compute the average number of arrivals per hour. Select the random numbers needed from the first col- umn of Table 4. beginning with the digits 52. 3. The University of South Wisconsin has had steady en- rollments over the past 5 years. The school has its own bookstore, called University Book Store, but there are also three private bookstores in town: Bill's Book Store, College Book Store, and Battle's Book Store. The university is concerned about the large number of students who are switching to one of the private stores. As a result, South Wisconsin's president, Andy Lange, has decided to give a student 3 hours of uni- versity credit to look into the problem. The following matrix of transition probabilities was obtained: UNIVERSITY BILL'S COLLEGE BATTLE'S UNIVERSITY 0.6 0.2 0.1 0.1 BILL'S 0.7 0.2 0.1 COLLEGE 0.1 0.1 0.8 BATTLE'S 0.05 0.05 0.1 0.8 At the present time, each of the four bookstores has an equal share of the market. What will the market shares be for the next period? 4. The cellular phone industry is very competitive. Two companies in the greater Lubbock area, Horizon and Local Cellular, are constantly battling each other in an attempt to control the market. Each company has a 1-year service agreement. At the end of each year, some customers will renew, while some will switch to the other company. Horizon customers tend to be loyal, and 80% renew, while 20% switch. About 70% of the Local Cellular customers renew, and about 30% switch to Horizon. If there are currently 100,000 Horizon customers and 80,000 Local Cel- lular customers, how many would we expect each company to have next year?

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