1The 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.
- True
- False
2You 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 / ExpectedValue
Proceed with testing / -12,000 / 2,500 / 15,000
Decide not to test / 0 / 0 / 0
Calculate the expected values to proceed with testing and to decide not to test, respectively.
- 250, 0
- 250, 100
- 650, 0
- 800, 0
- 800, 100
Value
Proceed with testing / -12,000 / 2,500 / 15,000 / 650
Decide not to test / 0 / 0 / 0 / 0
=1-.5-.2
=.3 / .5 / .2
3When calculating the expected value of perfect information, “perfect information” refers to knowing in advance when each of the possible states of nature will occur.
- True
- False
4Utilization of Bayes' Theorem permits decision-makers to work with revised probabilities, which are known as:
- prior probabilities
- marginal probabilities
- utility numbers
- expected monetary values (EMV)
- posterior probabilities
5A 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.
- True
- False
The survey is worth $65,000 - $62,000 = $3000
6Before 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?
- 0.10
- 0.37
- 0.50
- 0.71
- 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 / Successful / Unsuccessful / ProbabilityFavorable / P(F&S)=
P(FIS)*P(S)=
.90(.5)=.45 / P(F&U)=
P(F/U)*P(U)=
.20(.5)=.10 / P(F)=.55
Not Favorable / P(N&S)=
P(N/S)*P(S)=
.10(.5)=.05 / P(N&U)=
P(N/U)*P(U)=
.80(.5)=.40 / P(N)=.45
Probability / P(S)=0.50 / P(U)=0.50 / 1.00
P(S/F) = P(F&S)/P(F)=.45/.55=.818=.82
7In decision analysis, the actual events that may occur in the future over which the decision maker has no control are known as:
- States of nature
- Alternatives
- Payoffs
- Criteria
- Posteriors
8In decision analysis, when probabilities can be assigned to the occurrence of states of nature in the future, the situation is referred to as:
- Decision making under uncertainty
- Expected value of perfect information
- Decision making under risk
- Expected value under uncertainty
9A 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 / Low Rainfall / Moderate Rainfall / Heavy RainfallSoybeans / 18 / 88 / 48
Corn / -2 / 85 / 20
Wheat / 2 / 82 / 30
What alternative would be chosen if the maximin criterion is used?
- Plant soybeans
- Plant corn
- Plant wheat
- Moderate rainfall
- 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.)
10A state of nature is a future event that we have control over.
- True
- False
11A Maximin decision is more likely to be made by someone who is risk averse
than by someone who is a risk taker.
- True
- False
12The Expected Value with Perfect Information (EVwPI) can be determined
without using probabilities.
- True
- False
13Bayes’ Theorem can be used to combine prior probabilities of events with
market research results.
- True
- False
14Salvage value is realized when the production quantity exceeds the demand.
- True
- False
15When solving a decision tree, expected values are computed at decision nodes.
- True
- False
16If 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 =
- 0.5
- 1
- 50
- 100
- 150
=100/(1200-1000)
17Selling 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.
- = 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
18Using the following joint probability table, find P(A1/B2):
B1B2P(A)
A1.10.20 .30
A2.40.30 .70
P(B).50.501.00
- .10 b. .30 c. .33 d. .40 e. .50
19Consider the following payoff (profit) table. Which decision would be selected by aperson using Maximin as a criteria?
Decision / States of / Nature1 / 2 / 3 / 4 / 5
A
/ 20 / 40 / 60 / 80 / 100B / 2 / 92 / 2 / 2 / 2
C / -50 / 92 / 94 / 96 / 98
a. A
b. B
c. C
d. A and B
e. B and C
20In 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,
- .1*2 + .2*40 + .5*2 + .1*2 + .1*2
- .1*2 + .2*92 + .5*2 + .1*2 + .1*2
- .1*(-50) + .2*92 + .5*94 + .1*96 + .1*100
- .1*20 + .2*40 + .5*60 + .1*80 + .1*100
- .1*20 + .2*92 + .5*94 + .1*96 + .1*100