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

by OC2355802

Department

ManagementCourse Code

MGOC10H3Professor

Vinh QuanStudy Guide

FinalThis

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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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