At the end of the first year, Ellie will either reinvest the entire amount plus the return or sell and take the profit or loss. If she reinvests, she estimates that there is a .60 probability the market will go up and a .40 probability the market will go down.

MEM 505 Assignment 3
Problem 1: An oil exploration company has to decide between three sites in which to invest in its next drilling
project. The decision to drill in a region is determined by oil prices and the cost of setting up the drill. If oil
prices are high, it is worth drilling in remote locations, whereas if prices are low, it is better to minimize the
investment to guarantee profits. The table below summarizes the different profits given oil prices.
Million $
State of nature
Low Medium High
North Sea
Brazil offshore
Russia
3,000
300
1,500
2,000
2,500
4,000
1,000
5,000
2,200
Determine the best investment according to the following decision criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Equal likelihood
Problem 2: The Loebuck Grocery must decide how many cases of milk to stock each week to meet demand.
The probability distribution of demand during a week is shown in the following table:
Demand (cases) 15 16 17 18
Probability .20 .25 .40 .15
Each case costs the grocer $10 and sells for $12. Unsold cases are sold to a local farmer (who mixes the milk
with feed for livestock) for $2 per case. If there is a shortage, the grocer considers the cost of customer will
and lost profit to be $4 per case. The grocer must decide how many cases of milk to order each week.
a. Construct the payoff table for this decision situation.
b. Compute the expected value of each alternative amount of milk that could be stocked and select the
best decision.
c. Construct the opportunity loss table and determine the best decision.
d. Compute the expected value of perfect information.
Problem 3: Ellie Daniels has $200,000 and is considering three mutual funds for investment—a global fund,
an index fund, and an Internet stock fund. During the first year of investment, Ellie estimates that
there is a .70 probability that the market will go up and a .30 probability that the market will go down.
Following are the returns on her $200,000 investment at the end of the year under each market condition:
Million $
Market conditions
Up Down
Global
Index
Internet
$25,000
35,000
60,000
$–8,000
5,000
–35,000
At the end of the first year, Ellie will either reinvest the entire amount plus the return or sell and take the
profit or loss. If she reinvests, she estimates that there is a .60 probability the market will go up and a .40
probability the market will go down. If Ellie reinvests in the global fund after it has gone up, her return on her
initial $200,000 investment plus her $25,000 return after 1 year will be $45,000. If the market goes down,
her loss will be $15,000. If she reinvests after the market has gone down, her return will be $34,000, and her
loss will be $17,000. If Ellie reinvests in the index fund after the market has gone up, after 2 years her return
will be $65,000 if the market continues upward, but only $5,000 if the market goes down. Her return will be
$55,000 if she reinvests and the market reverses itself and goes up after initially going down, and it will be
$5,000 if the market continues to go down. If Ellie invests in the Internet fund, she will make $60,000 if the
market goes up, but she will lose $35,000 if it goes down. If she reinvests as the market continues upward,
she will make an additional $100,000; but if the market reverses and goes down, she will lose $70,000. If she
reinvests after the market has initially gone down, she will make $65,000, but if the market continues to go
down, she will lose an additional $75,000.
Using decision tree analysis, determine which fund Ellie should invest in and its expected value