• Please follow the instructions (upload 4 files) (don’t upload compressed zip files)

• Please provide your answers as a pdf file (one file)

• Upload an excel file with your simulations (create a tab for each problem) (one file)

• Upload a Bayesian Belief Network model for each problem (2 files)

• This exam is to be completed individually. Any collaboration will automatically result in a 0.

• Make sure that you upload your own work, plagiarized material result in a 0 for THE SUBJECT and an F for the course

• Late uploads will incur a 10 point penalty for each day the upload is late (no exceptions)

Problem 1

Giant Foods has decided to make 25 roasted chickens for the lunch rush. The store has determined that daily demand will follow the distribution shown in the following table:

Daily Demand Probability
10 0.07
15 0.12
20 0.26
35 0.21
30 0.20
35 0.14

Each chicken costs Giant Foods $5.50 to make and can be sold for $12. It is possible for Giant Foods to sell any unsold chickens for $5 the next day (assume all unsold chickens are sold the next day regardless of demand).

a. Simulate one month (30 days) of operation to calculate Giant Food’s total monthly roasted chicken profit. Replicate this calculation 50 times to compute the average total monthly profit.

b. Giant Foods would like to verify the profitability of making 10, 20, 30, or 40 chickens during the lunch rush. Which quantity would you recommend? Why?

Problem 2

There are burglar alarms that are meant to detect opening doors and motion, which occurs 3% of the time. The alarms have identical specifications with a false positive rate of 2 % and a false negative rate of 4%. If the telephone signal is off, the alarms will read negative regardless of the door status. Suppose now that we have two different alarm sets:

Set 1: each alarm is connected to a unique phone line

Set 2: both alarms are connected to the same phone line

Assuming that each phone line has a .78 probability of having signal, what is the probability of door open and motion detected given each of the following scenarios (Answer the following questions for each set):

(a) The two alarms read negative

(b) The two alarms read positive

(c) Motion alarm reads positive while the door reads negative.

Problem 3

Kirkpatrick Aircrafts operates a large number of computerized plotting machines. For the most part, the plotting devices are used to create line drawings of complex wing airfoils and fuselage part dimensions. The engineers operating the automated plotters are called loft lines engineers.

The computerized plotters consist of a minicomputer system connected to a 4×5-foot flat table with a series of ink pens suspended above it. When a sheet of clear plastic or paper is properly placed on the table, the computer directs a series of horizontal and vertical pen movements until the desired figure is drawn.

The plotting machines are highly reliable, with the exception of the three sophisticated ink pens that are built in. The pens constantly clog and jam in a raised or lowered position. When this occurs, the plotter is unusable.

Currently, Kirkpatrick Aircrafts replaces each pen as it fails. The service manager has, however, proposed replacing all three pens every time one fails. This should cut down the frequency of plotter failures. At present, it takes one hour and a half to replace one pen. All three pens could be replaced in two and a half hours. The total cost of a plotter being unusable is $600 per hour. Each pen costs $76. The following breakdown data are thought to be valid:

One Pen Replaced Three Pens Replaced
Hours Between Failures Probability Hours Between Failures Probability
15 0.12 90 0.05
25 0.15 100 0.12
35 0.17 110 0.24
45 0.21 120 0.32
55 0.20 130 0.21
65 0.15 140 0.06

a. For each option (replacing one pen at a time and replacing all three pens at a time), simulate the average total time a plotter would operate before it would have 20 failures. Then compute the total cost per hour for each option to determine which option Kirkpatrick Aircrafts should use. Use 200 replications.

b. Compute the total cost per hour analytically for each option. How do these results compare with the simulation results?

Problem 4

The world of Formula racing is very exciting but predictable. Lewis Hamilton is winning most races. Every time he wins a race, there is a probability of 85% that he will win the next race. He doesn’t win them all, if he doesn’t win; there is a 42% probability that he will lose the next race. The probability that he lost the last race is 52%, what is the probability that he won the last race since he won today.

Problem 5

Using the link below, write short paper (pdf) explaining how the information from the news report could be used to identify uncertainties and identify the decisions associated with the uncertainties that could be facilitated by developing a risk model.

Identify risks

1. Identify an area of uncertainty

2. Select a focus area related to that uncertainty

3. Identify 3 risk areas

4. Identify 2 risks associated with the news article (Remember that risks are stated based on impact and likelihood)

a. If __________, then ____________

5. Identify 10 variables that could potentially affect the risks identified

a. Identify possible data sources for those variables

6. Discuss how the development of a risk model helps the decision making process derived from the risks identified

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