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

by OC1216667

Department

ManagementCourse Code

MGOC10H3Professor

Vinh QuanStudy Guide

FinalThis

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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)

Given

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

Find

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)

Path

payoff

prob

test, positive, no let in

-100

0.08

test, negative, let in, disease

-100,100

(1/46)*0.92=.02

test, negative, let in, no disease

9900

(45/46)*0.92=.9

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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