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MGOC10H3 Study Guide - Final Guide: Feasible Region, Radiography, Perfect InformationExam

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Vinh Quan
Study Guide

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Department of Management, UTSC
MGOC10 Analysis for Decision Making - Practice Problem Set 2 Solution
Problem 1
The government is attempting to determine whether immigrants should be tested for a disease. Let’s assume that the
decision will be made based on a financial basis. Each immigrant who is allowed into the country and has the disease
costs Canada $100,000 and each person who does not have the disease contributes $10,000 to the economy. 10% of all
potential immigrants have the disease. The government may admit all immigrants, no immigrants or test immigrants for
disease before deciding they should be admitted. It costs $100 to test a person for the disease. The test result is either
positive or negative. Given the test result is positive, the person definitely has the disease. Given the person who has the
disease, there is a 20% they will test negative. Given a person who does not have the disease, they always test negative.
(a) Assuming the government’s goal is to maximize expected benefits from immigrants, use a decision tree to determine
what it should do and the expected benefits. (10 marks)
P[has Disease] = 0.1, P[No disease] = 0.9
P[test negative | disease ] = 0.2 → P[test positive | disease ] = 0.8
P[has disease | test positive] = 1 → P[no disease | test positive] = 0
P[test negative | no disease] = 1 → P[test positive | no disease] = 0
P[test positive]=p[test positive | disease]p[disease] + p[test positive | no disease]p[no disease] = (0.8)(0.1)+(0)(0.9) = 0.08
→ P[test negative] = 0.92
P[has disease | test negative] = (0.2)(0.1) /(0.92) = 1/46 → P[no disease | test negative] = 45/46
Test each immigrant for the disease. Let in immigrants who test negative, but don't let in immigrants who test positive
Expected benefit = $6900

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(b) Calculate the Expected Value of Perfect Information. (4 marks)
With no info payoff = 0, With perfect info payoff = $9000, EVPI = 9000 0 =$9000
(c) Provide a risk profile for your answer in (a)? (4 marks)
test, positive, no let in
test, negative, let in, disease
test, negative, let in, no disease
Problem 2
Alden Construction is bidding against Forbes Construction for a project. Alden believes that Forbes bid will be either
$6000, $8000 or $11000. If Alden wins and gets to do the project, it will cost Alden $6000 to complete the project. So if
Forbes bids $11000 and Alden bid $8000, then Alden wins the project and earns $2000 profits. Assume that if Alden’s bid
is tie with Forbes bid, then Alden gets the project. How much should Arden bid if Arden was to use a Minimax Regret
approach. (Hint: Alden should only consider bidding either $6000, $80000 or $11000) (6 marks)
The payoff & regret matrix is
Alden' Bid
$6,000 $8,000 $11,000
Forbes Bid
$6,000 $0 $0 $0
$8,000 $0 $2,000 $0
$11,000 $0 $2000 $5,000
Alden' Bid
Forbes bid $6,000 $8,000 $11,000
$6000 0 0 0
$8,000 2000 0 2000
$11,000 5000 $3000 0
Max 5000 3000 2000*
Thus Minimax regret action is to bid $11,000.
Problem 3
During the summer, Olympic swimmer Bruce Lee swims every day. On sunny summer days, he goes to an outdoor pool,
where he may swim for no charge. On rainy days, he must go to a domed pool. At the beginning of the summer, he has
the option of purchasing a $15 season pass to the domed pool, which allows him use for the entire summer. If he doesn’t
buy the season pass, he must pay $1 each time he goes there. Past meteorological records indicate that there is a 60%
chance that the summer will be sunny (in which case there is an average of 6 rainy days during the summer) and a 40%
chance the summer will be rainy (an average of 30 rainy days during summer). Before the summer begins, Bruce has the
option of purchasing a long-range weather forecast for $1. The forecast predicts a sunny summer 80% of the time and a
rainy summer 20% of the time. If the forecast predicts a sunny summer, there is a 70% chance that the summer will
actually be sunny. If the forecast predicts a rainy summer, there is an 80% chance that the summer will actually be rainy.
(a) Assuming Bruce’s goal is to minimize his expected cost for the summer, use a decision tree to determine what he
should do and the expected cost. (8 marks)

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From tree, he should buy forecast. If forecast says sunny, he should not buy pass. If forecast says rainy, he should
buy pass. Expected cost is $14.56.
Both version of the tree is correct as they have the same logic. I personally prefer second tree as it is more simple.
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