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Modeling and Simulation

Anwer the following questions in the attached file:

Problem 15-14
Problem 15-16
Problem 15-17 - See the separate attachment for Solve Problem 15-1

(15-14) Clark Property Management is responsible for the 4 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 compressors. He would like to simulate the number of compressor failures each year over the next 20 years. Using data from a similar apartment building he manages in a New Orleans suburb, Clark establishes a table of relative frequency of failures during a year as shown in the following table:

Number of A.C. Compressor Failures Probability (Relative Frequency)
0 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 20-year period by selecting two-digit random numbers from the third column of Table 15.5, 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?

(15-16) Compute the expected number of cars arriving in Problem 15-15 using the expected value formula. Compare this with the results obtained in the simulation.

(15-17) Refer to the data in Solved Problem 15-1, which deals with Higgins Plumbing and Heating. Higgins has now collected 100 weeks of data and finds the following distribution for sales:

Hot Water Heater Sales Per Week Number of Weeks This Number Was Sold
3 2
4 9
5 10
6 15
7 25
8 12
9 12
10 10
11 5

(a) Resimulate the number of stockouts incurred over a 20-week period (assuming Higgins maintains a constant supply of 8 heaters).
(b) Conduct this 20-week simulation two more times and compare your answers with those in part (a). Did they change significantly? Why or why not?
(c) What is the new expected number of sales per week?