1
The expected value of perfect information places an upper bound as to what one
might be willing to pay for additional information to aid in making a decision.
a. True
b. False
2
You have the following expectations based on your analysis of a process. You
believe that there is a 50% chance of being moderately effective and a 20% chance
of being highly effective: You are trying to decide whether to do testing before
making a decision.
Ineffective
Moderately
Effective
Highly
Effective
Proceed
with testing
-12,000
2,500
15,000
Decide not
to test
0
0
0
Expected
Value
Calculate the expected values to proceed with testing and to decide not to test,
respectively.
a. 250, 0
b. 250, 100
c. 650, 0
d. 800, 0
e. 800, 100
Proceed
with testing
Decide not
to test
Ineffective
Moderately
Effective
Highly
Effective
Expected
Value
-12,000
2,500
15,000
650
0
0
0
.5
.2
=1-.5-.2
=.3
3
=-12,000*.3
+2,500*.5
+15,000*.2
=650
0
=0*.3
+0*.5
+0*.2
=0
When calculating the expected value of perfect information, “perfect information”
refers to knowing in advance when each of the possible states of nature will occur.
a. True
b. False
4
Utilization of Bayes' Theorem permits decision-makers to work with revised
probabilities, which are known as:
a. prior probabilities
b. marginal probabilities
c. utility numbers
d. expected monetary values (EMV)
e. posterior probabilities
5
A market research survey is available for $10,000. Using a decision tree analysis,
it is found that the expected monetary value with the survey is $65,000. The expected
monetary value with no survey is $62,000. Based on this information, the survey should
be taken.
a. True
b. False
The survey is worth $65,000 - $62,000 = $3000
6
Before a marketing research study was done, John Colorado believed there was a
50/50 chance that his music store would be a success. The research team determined
that there is a 0.9 probability that the marketing research will be favorable given a
successful music store. There is also a 0.8 probability that the marketing research will
not be favorable given an unsuccessful music store. If the marketing research is
favorable, what is the revised probability of a successful music store?
a. 0.10
b. 0.37
c. 0.50
d. 0.71
e. 0.82
[S=Successful, U=Unsuccessful, F=Favorable, N=Not Favorable; P(S)=.50,
P(U)=.50; P(F/S)=.90, therefore P(N/S)=.10; P(N/U)=.80, therefore, P(F/U)=.20;
Using Bayes’ Theorem, P(A|B) = P(B|A)*P(A)/[P(B|A1)*P(A1) + P(B|A2)*P(A2)]:
P(S|F) = P(F|S)*P(S)/[P(F|S)*P(S) + P(F|U)*P(U)]=(.90)(.50)/[(.9)(.50)+(.20)(.50)]
= .45/(.45 + .10) = .45/.55 = .82
Or, using a Joint Probability Table to calculate P(S/F).]
Joint
Probability
Table
Favorable
Not
Favorable
Probability
Successful
Unsuccessful
P(F&S)=
P(FIS)*P(S)=
.90(.5)=.45
P(N&S)=
P(N/S)*P(S)=
.10(.5)=.05
P(F&U)=
P(F/U)*P(U)=
.20(.5)=.10
P(N&U)=
P(N/U)*P(U)=
.80(.5)=.40
P(S)=0.50
P(U)=0.50
Probability
P(F)=.55
P(N)=.45
1.00
P(S/F) = P(F&S)/P(F)=.45/.55=.818=.82
7
In decision analysis, the actual events that may occur in the future over which the
decision maker has no control are known as:
a.
b.
c.
d.
e.
States of nature
Alternatives
Payoffs
Criteria
Posteriors
8
In decision analysis, when probabilities can be assigned to the occurrence of
states of nature in the future, the situation is referred to as:
a. Decision making under uncertainty
b. Expected value of perfect information
c. Decision making under risk
d. Expected value under uncertainty
9
A continuing drought has caused concern for a farmer who must decide whether to
plant soybeans, corn, or wheat. The table below shows the farmer's expected profit
($000s) depending on the crop planted and amount of rainfall that occurs.
Alternative
Soybeans
Corn
Wheat
Low Rainfall
18
-2
2
Moderate Rainfall Heavy Rainfall
88
48
85
20
82
30
What alternative would be chosen if the maximin criterion is used?
a. Plant soybeans
b. Plant corn
c. Plant wheat
d. Moderate rainfall
e. Heavy rainfall
[The worst outcome for soybeans, corn, and wheat is 18, -2, and 2,
respectively; therefore, the best of the worst is 18; therefore, soybeans is
the maximin strategy.)
10
A state of nature is a future event that we have control over.
a. True
b. False
11
A Maximin decision is more likely to be made by someone who is risk averse
than by someone who is a risk taker.
a. True
b. False
12
The Expected Value with Perfect Information (EVwPI) can be determined
without using probabilities.
a. True
b. False
13
Bayes’ Theorem can be used to combine prior probabilities of events with
market research results.
a. True
b. False
14
Salvage value is realized when the production quantity exceeds the demand.
a. True
b. False
15
When solving a decision tree, expected values are computed at decision nodes.
a. True
b. False
16
If EVSI = 100, EVBest = 1000 (this is the best decision), and EVc = 1200 (this is
the best possible return, which would be used to calculate EVPI), then Efficiency =
a. 0.5
b. 1
c. 50
d. 100
e. 150
=100/(1200-1000)
17
Selling price per unit is $45;
Variable cost per unit is $5;
Salvage value per unit is $2 (this is the per piece value of undemanded
products);
Cost of lost sales is $1.
Find the profit when 60 units are produced and the state
of nature is a demand of 40 units. Do not include fixed costs.
a.
b.
c.
d.
e.
18
 = 45*40 - 5*40 - 1*20
 = 45*40 - 5*60 + 2*20
 = 45*60 - 5*40 - 1*20
 = 45*40 - 5*60 + 2*20 - 1*20
 = 45*60 - 5*40 + 2*20 - 1*20
Using the following joint probability table, find P(A1/B2):
A1
B1
.10
B2
.20
P(A)
.30
=.20/.50
A2
P(B)
a. .10
19
.40
.50
b. .30
c. .33
.70
1.00
d. .40
e. .50
Consider the following payoff (profit) table. Which decision would be selected by
a person using Maximin as a criteria?
Decision
A
B
C
a.
b.
c.
d.
e.
20
.30
.50
1
20
2
-50
States
of
2
40
92
92
Nature
3
60
2
94
4
80
2
96
5
100
2
98
A
B
C
A and B
B and C
In the previous payoff (profit) table above, what is the EVc given the following
probabilities?
P(1) = .1; P(2) = .2; P(3) = .5; P(4) = .1; P(5) = .1,
a. .1*2 + .2*40 + .5*2 + .1*2 + .1*2
b. .1*2 + .2*92 + .5*2 + .1*2 + .1*2
c. .1*(-50) + .2*92 + .5*94 + .1*96 + .1*100
d. .1*20 + .2*40 + .5*60 + .1*80 + .1*100
e. .1*20 + .2*92 + .5*94 + .1*96 + .1*100