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MGOC10H3 Lecture Notes - Lecture 3: Test Pilot, Decision Tree Learning, Conditional ProbabilityExam


Department
Management
Course Code
MGOC10H3
Professor
Vinh Quan
Study Guide
Final

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1
MGOC10 Analysis for Decision Making
Lecture 09
Chapter13 Decision Analysis - Decision Trees
Example 1
Peso Co. has $150K and deciding whether to launch a new soda in Canada. Peso feels that there
is a 0.55 chance that it will be a success. If successful, Peso will earn $300K, if failure, it loses
$100K. For a cost of $30K, Peso can hire a marketing firm to test trial the soda in Toronto.
Peso feels that there is a 60% chance that Torontonians will like the soda. Based on past soda’s
launch, if Toronto likes a soda, then there is an 85% chance Canada will also like the soda. If
Toronto does not like a soda, there is a 10% chance Canada will still like it.
(a) What should Peso do to maximize expected asset position? Use a decision tree to analyze.
(b) Provide the risk profile for the optimal decision.
(c) Provide the risk profile for the decision to test pilot.
(d) What is the max amount of money you would pay for the pilot?
(e) What is the max amount of money you would pay to find out for sure if success or not?
Example 2
Fruit Computer Company manufactures memory chips in batches of 10 chips. From past
experience, Fruit knows that 80% of all batches contain 10% defective chips, and 20% of all
batches contain 50% defective chips. If a good (that is, 10% defective) batch of chips is sent to
next stage of production, processing cost of $1000 are incurred, and if a bad batch (50%
defective) is sent, processing costs of $4000 are incurred. Fruit also has the alternative of
reworking a batch at a cost of $1000 before sending onto next stage. A reworked batch is sure to
be a good batch. Also, for a cost of $100, Fruit can test one chip from each batch in an attempt
to determine whether the batch is bad.
(a) Assuming Fruit’s goal is to minimize his expected cost per batch, use a decision tree to
determine what he should do and the expected cost.
(b) Provide the risk profile for the optimal decision.
(c) What is the max amount of money you would pay to test a chip?
(d) What is the max amount of money you would pay to find out for sure if batch is good or bad?
(e) Suppose that Fruit produces good (10% defect), average (25% defect) and bad batches
(50% defect) with probabilities 0.65, 0.2 and 0.15 respectively. Determine the probability of
getting a defective chip. Determine the probability that the batch is good, average and bad
given a defective chip found.
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