# Qouintitive method

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
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
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