Part 1:

A high school student is considering different career paths and wants to make the right decision.

The student is aware that with a higher salary comes more stress. The following table gives

projected salary for each career based on stress levels.

High Stress

Comic Book Artist $220,000 $160,000 $80,000

Financial Advisor $260,000 $140,000 $60,000

University Professor $240,000 $160,000 $100,000

Mechanical Enineer $160,000 $140,000 $120,000

1. Make a decision tree and show how the student’s choice would change based on the following

approaches:

a) Optimistic Approach

b) Conservative Approach

c) Minimax Regret Approach

2. If the probability of high stress levels is 0.65 and probability of low stress levels is 0.15, what

career should the student choose? Show Expected Value for all nodes. What is the Expected

Value of Perfect Information?

Part 2:

The Toronto Maple Leafs want to make a change to turn the season around and are considering

two options. There is a chance that each could result in positive or negative feedback from the

fan base. The table gives viewers per game based on the decision and outcome.

Positive Feedback Negative Feedback

Fire Coaching Staff 900,000 fans 300,000 fans

Trade Core Player 700,000 fans 500,000 fans

The prior probability for positive feedback without research is 0.6. To make a decision the

management group had team personnel do some research into the two alternatives.

They have found the following:

o The probability of unfavourable research given positive feedback is 0.28

o The probability of unfavourable research given negative feedback is 0.82

1. Find the Expected Value of for each possible combination. What is the Expected Value of

Sample Information and how efficient is the research? What is your recommendation to the

management team of the Toronto Maple Leafs to increase viewers?

Question 1

Chelsea and Arsenal are completing with each other to sign a soccer player. They both

believe that obtaining this player would increase viewership of their games. The

following table shows how strategies would affect the number of Viewers for Chelsea’s

games.

Positives are increases of

viewers for Chelsea. Playing Time Perks (Car)

200,000 700,000 400,000

Chelsea Playing Time -600,000 400,000 -300,000

Perks (Car) -400,000 -ZOo,000 -lOo,000

Find the pure strategy for this two-person, zero-sum game. Who would have the

advantage?

Question 2

How would the game change if they both decided to offer the same amount of money?

Find the new solution to the game. Who would have the advantage?

Question 3

The manufacturers of Right Twix and Left Twix are in competition with each other to

increases sales of their half of the chocolate bar. The following table shows the strategies

each manufacturer is considering and the outcome in increase of sales.

infrease if‘ sales for Change Celebrity New Cookie

nght TW1X Chocolate Endorsement Recipe

Change 130,000 -130,000 140,000

Caramel

ngl‘t New. -140,000 110,000 -120,000

TW1X Packaging

140,000 -110,000 150,000

Promotion

Determine if a pure strategy can be found for the game. Eliminate any dominated

strategies. Find the solution to the reduced game and determine who would have the

advantage. What would be your recommendation to each manufacturer?