Decision Analysis – Prac Prob 2015

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Decision

Analysis

– Practice

Problems

DMUO ‐ 2015

Dr. Gunjan Malhotra

[email protected]; [email protected]

9/8/2015 1IMT, Ghaziabad, INDIA



Question 1. • Bob’s bike shop is considering three options for its facility next year.

Bob can expand his current shop, move to a larger facility, or make no change. With a good market, the annual payoff would be

$56,000 if he expands, $70,000 if he moves, and $30,000 if he does nothing. With an average market, his payoffs will be $21,000, $35,000, and $10,000, respectively. With a poor market, his payoff will be ‐$29,000, ‐$45,000, and $5,000 respectively.

(a) Which option should Bob choose if he uses the maximax criterion?

(b) Which option should Bob choose if he uses the maximin criterion?

(c) Which option should Bob choose if he uses the equally likely criterion?

(d) Which option should Bob choose if he uses the criterion of realism

with α =0.6?

(e) Which option should Bob choose if he uses the minimax regret criterion?



Answer 1. (a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.6)

Alternatives Maximum Choice Minimum Choice Average Choice Realism Choice

Expand $56,000 -$29,000 $16,000 $22,000Move $70,000 Best -$45,000 $20,000 Best $24,000 Best

No change $30,000 $5,000 Best $15,000 $20,000

egret Outcomes (e) Minimax

lternatives Good Average Poor Maximum Choice

xpand $14,000 $14,000 $34,000 $34,000 Best

ove $0 $0 $50,000 $50,000o change $40,000 $25,000 $0 $40,000



Question 2.• Bob (in continuation to the previous question)

has gathered some additional information. The probabilities of good, average, and poor markets are 0.25, 0.45, and 0.3, respectively.

• (a) Using EMVs, what option should Bob choose?

What is the maximum EMV?

• (b) Using EOL, what option should Bob choose?

What is the minimum EOL?• (c) Compute the EVPI and show that it is the

same as the minimum EOL.



Answer 2.

Alternatives EMV Choice

Expand $14,750 Move $19,750 Best

No change $13,500

Expected Value WITH Perfect Information (EVwPI) = $34,750

Best Expected Monetary Value (EMV) = $19,750Expected Value OF Perfect Information (EVPI) = $15,000

Alternatives EOL ChoiceExpand $20,000

Move $15,000 Best

No change $21,250



Question 3.• Jeff Park sells newspapers on Sunday mornings in an area

surrounded by three busy churches. Assume that Jeff’s demand can

either be for 100, 200, or 300 newspapers, depending on traffic and

weather. Jeff has the option to order 100, 200, or 300 newspapers from his supplier. Jeff pays$1.25 for each newspaper he orders and

sells each for $2.00.

• (a) How many papers should Jeff order if he chooses the maximax criterion?

• (b) How many papers should Jeff order if he chooses the maximin

criterion?

• (c) How many papers should Jeff order if he chooses the equally likely criterion?

• (d) How many papers should Jeff order if he chooses the criterion

of realism α =0.4?

• (e) How many papers should Jeff order if he chooses the minimax regret criterion?



Answer 3.

(a) Maximax (b) Maximin

(c) Equally

Likely

(d) Hurwicz

(0.4) (e) MinimaxAlternatives

Maximum

Choice

Minimum

Choice Average Choice Realism Choice

Maximum

Choice

100 $75 $75 Best $75 $75 Best $150

200 $150 -$50 $83 Best $30 $125 Best

300 $225 Best -$175 $25 -$15 $250



Question 4.• Jeff Park (in continuation to question 3) has done

some research and discovered that the probabilities for demands of 100, 200, and 300

newspapers are 0.4, 0.35, and 0.25, respectively.

• (a) Using EMVs, how many paper should Jeff

order?

•

(b)

Using

EOL,

how

many

paper

should

Jeff

order?

• (c) Compute Jeff’s EVwPI and EVPI.



Answer 4.

Alternatives EMV Choice100 $75 Best200 $70300 -$5

Expected Value WITH Perfect Information (EVwPI) = $139Best Expected Monetary Value (EMV) = $75Expected Value OF Perfect Information (EVPI) = $64

Alternatives EOL Choice100 $64 Best200 $69300 $144



Question 5.• Even though independent gasoline stations have been having a difficult time,

Susan Solomon has been thinking about starting her own independent gasoline

station. Susan’s problem is to decide how large her station should be. The annual

returns will depend on both the size of her station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis,

Susan developed the following payoff (profit) table:

• (a) what is the maximax decision?

• (b) what is the maximin decision?

• (c) what is the equally likely decision?

• (d) what is the criterion of realism decision, using α = 0.8?

• (e) what is the minimax regret decision?

Size Good Market ($) Fair Market ($) Poor Market ($)

Small 50,000 20,000 ‐10,000

Medium 80,000 30,000 ‐20,000

Large 1,00,000 30,000 ‐40,000

Very Large 3,00,000 25,000 ‐1,60,000



Answer 5.

(a) Maximax (b) Maximin(c) Equally

Likely(d) Hurwicz

(0.8) (e) Minimax

Alternatives

Maximum

Choice Minimum

Choice Average Choice Realism Choice

Maximum

Choice

Small $50,000 -$10,000 Best $20,000 $38,000 $250,000

Medium $80,000 -$20,000 $30,000 $60,000 $220,000

Large $100,000 -$40,000 $30,000 $72,000 $200,000

Very large $300,000 Best-

$160,000 $55,000 Best $208,000 Best $150,000 Best



Question 6.•

Kenneth

Brown

is

the

principal

owner

of

Brown

Oil,

Inc.

After

quitting

his

university

teaching job, ken has been able to increase his annual salary by a factor of over 100. At the present time, ken is forced to consider purchasing some more equipment for Brown Oil because of competition. His alternatives, outcomes, and payoffs (profits) are shown in the following table:

• (a) Ken has always been very optimistic decision maker. Which alternative is best from Ken’s point of view?

• (b) Although ken is the principal owner of Brown Oil, his brother Bob is credited

with making the company a financial success. Bob attributes his success to his pessimistic attitude about business and the oil industry. Which alternative is best from Bob’s point of view?

• (c) The Lubricant is an expensive oil newsletter to ken subscribes. In the latest issue, the newsletter describes how the demand for oil products will be extremely high. Apparently, the American consumer will continue to use oil products even if the price of these products doubles. Indeed, one of the articles in the Lubricant states that the chance of a favourable market for oil products is 70%. If ken uses these

probabilities

in

determining

the

best

decision,

which

alternative

is

best?

Equipment Favorable market ($) Unfavorable market ($)

Sub 100 300,000 ‐200,000

Oiler J 250,000 ‐ 100,000

Texan 75,000 ‐18,000



Answer 6.

Outcomes (a) Maximax (b) Maximin (c) EMV

Alternatives Fav mkt Unfav mkt Maximum Choice Minimum Choice EMV Choice

Sub 100 $300,000 -$200,000 $300,000 Best -$200,000 $150,000 Best

Oiler J $250,000 -$100,000 $250,000 -$100,000 $145,000

Texan $75,000 -$18,000 $75,000 -$18,000 Best $47,100



• DECISION TREES



Question 7.• A group of medical professionals is considering constructing a private clinic. If patient demand for the clinic is high, the physicians could realize a net profit of $100,000. If the demand is low, they could lose $40,000. Of course, they don’t have to proceed at all, in which case there is no cost. In

the absence of any market data, the best the physicians can guess is that there is a 50‐50 chance that demand will be good.

• (a) construct a decision tree to help analyze this problem. What should the medical professionals do?

• (b) The physicians have been approached by a market research firm that

offers to perform a study of the market at a fee of $5,000. The market researchers claim that their experience enables them to use Bayes’ theorem to make the following statements of probability:

• Probability of high demand given a positive study result = 0.82

• Probability of low demand given a positive study result = 0.18

• Probability of high demand given a negative study result = 0.11• Probability of low demand given a negative study result = 0.89

• Probability of a positive study result = 0.55

• Expand the decision tree in part (a) to reflect the options now open with

the market study. What should the medical professionals do now?



Answer 7.• (a) EMV if we construct the clinic = 0.5 * $100,000 + 0.5 * (‐$40,000) =

$30,000. EMV if we do nothing = $0. Therefore, construct clinic.

•

• (b) Excel: Construct clinic if result is positive. Do not construct clinic if result is negative. EMV = $36,140

•

• (c) EVSI = $11,140. Thus, the physicians would pay up to $11,140 more for

the survey. Note: Since EVSI should be calculated assuming no

cost to

gather the sample information, $5,000 had to be added back to $36,140.

•

• (d) EVwPI = $50,000. Best EMV = $30,000. EVPI = $20,000. Efficiency = 55.70%.

•

•



Answer 7. 0.82

High demand

(a) Construct clinic; EMV = $30,000 $95,000

(b) Conduct study. Construct clinic if positive result Construct $1,00,000 $95,000

Do not construct clinic if negative result.

EMV = $36,140 $0 $69,800 0.18

(c) EVSI = $11,140 0.55 Low demand

(d) EVwPI = $50,000 Positive result -$45,000

Best EMV = $30,000 1 -$40,000 -$45,000

EVPI = $20,000 $0 $69,800

Efficiency = 55.70%Not Construct

-$5,000

$0 -$5,000

Study

0.11

-$5,000 $36,140 High demand

$95,000

Construct $1,00,000 $95,000

$0 -$29,600 0.89

0.45 Low demandNegative result -$45,000

2 -$40,000 -$45,000

$0 -$5,000

1 Not Construct

$36,140 -$5,000

$0 -$5,000

0.50

High demand$1,00,000

Construct $1,00,000 $1,00,000

$0 $30,000 0.50

Low demand

No Study -$40,000

1 -$40,000 -$40,000$0 $30,000

Not Construct

$0$0 $0

Problem 7



Question 8. • Jerry Young is thinking about opening a bicycle shop in his hometown. Jerry loves to

take his own bike on 50‐mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. Because there will be a five‐year lease on the building that Jerry is thinking about using, he wants to make sure

that he makes the correct decision.Jerry has done some analysis about the profitability of the bicycle shop. If

Jerry builds the large bicycle shop, he will earn $60,000 if the market is good, but he will lose $40,000 if the market is bad. The small shop will return a $30,000 profit in a good

market and a $10,000 loss in a bad market. At the present time, he believes that there is a 59% chance that the market will be good.

Jerry also has the option of hiring his old marketing professor for $5,000 to

conduct a marketing research study. If the study is conducted, the results could be either favorable or unfavorable. It is estimated that there is a 0.6 probability that the survey will be favorable. Furthermore, there is a 0.9 probability that the market will be good, given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of 0.12 of a good market if the marketing research results are not favorable.

• (a) Develop a decision tree for Jerry and help him to decide what he should do.

• (b) How much is the marketing professor’s information worth? What is the efficiency of this information>



Answer 8.• (a) Conduct survey. If results are favorable,

build large shop. If the results are unfavorable, don't build any shop.

•

• (b) EVSI = $11,000. EVwPI = $35,400. Best

EMV = $19,000. EVPI = $16,400. Efficiency =

67.07%.•



Answer 8. 0.59

Good market

(a) Conduct survey $60,000

If favorable, build large shop Large shop $60,000 $60,000

If unfavorable, don't build any shop

EVSI = $11,000 $0 $19,000 0.41

Bad market(b) EVwPI = $35,400 -$40,000

Best EMV = $19,000 -$40,000 -$40,000

EVPI = $16,400

Efficiency = 67.07% 0.59

Good marketNo survey $30,000

1 Small shop $30,000 $30,000

$0 $19,000

$0 $13,600 0.41

Bad market-$10,000

-$10,000 -$10,000

No shop$0

$0 $0

0.90

Good market$55,000

Large shop $60,000 $55,000

$0 $45,000 0.10

2 Bad market

$25,000 -$45,000

-$40,000 -$45,000

0.90

0.60 Good market

Favorable $25,000

1 Small shop $30,000 $25,000

$0 $45,000

$0 $21,000 0.10

Bad market

-$15,000

-$10,000 -$15,000

No shop-$5,000

$0 -$5,000

Survey

0.12-$5,000 $25,000 Good market

$55,000

Large shop $60,000 $55,000

$0 -$33,000 0.88

Bad market

-$45,000

-$40,000 -$45,000

0.12

0.40 Good market

Unfavorable $25,000

3 Small shop $30,000 $25,000

$0 -$5,000

$0 -$10,200 0.88

Bad market

-$15,000

-$10,000 -$15,000

No shop -$5,000

$0 -$5,000

Problem 8



Question

9.

Rob Johnson is a product manager for Diamond Chemical. The firm is considering whether to launch a new product line that will require building a new facility. The technology required to

produce the new product is yet untested. If Rob decides to build

the new facility and the process is successful, Diamond Chemical will realize a profit of $650,000. If the process does not succeed, the company will lose $800,000. Rob estimates that there is a

0.6 probability that the process will succeed.Rob can also decide to build a pilot plant for $50,000 to

test the new process before deciding to build the full – scale facility. If the pilot plant succeeds, Rob feels the chance of the

full‐scale facility succeeding is 85%. If the pilot plant fails, Rob feels the chance of the full‐scale facility succeeding is only 20%. The probability that the pilot plant will succeed is estimated at 0.6. Structure this problem with a decision tree and advise Rob what to do.



Answer

9.• Build the pilot plant. If the pilot plant

succeeds, build facility. If the pilot plant fails, don't build facility. Expected profit = $209,500.

•



Answer

9.0.85

Facility works

Build the pilot plant. $6,00,000

If pilot plant succeeds, build facility. Build facility $6,50,000 $6,00,000

If pilot plant fails, don't build facility.

Expected profit = $209,500 $0 $3,82,500 0.150.60 Facility fails

Pilot works -$8,50,0001 -$8,00,000 -$8,50,000

$0 $3,82,500

Don't build-$50,000

$0 -$50,000Build pilot

0.20

-$50,000 $2,09,500 Facility works

$6,00,000

Build facility $6,50,000 $6,00,000

$0 -$5,60,000 0.800.40 Facility fails

Pilot fails -$8,50,000

2 -$8,00,000 -$8,50,000

$0 -$50,000

Don't build

-$50,0001 $0 -$50,000

$2,09,5000.60

Facility works$6,50,000

Build facility $6,50,000 $6,50,000

$0 $70,000 0.40

Facility fails-$8,00,000

-$8,00,000 -$8,00,000

Do nothing

$0$0 $0

Problem 9



Question

10.• Rob Johnson (see problem 9) has some revised

information concerning the accuracy of the pilot plant probabilities. According to his new

information, the probability that the pilot plant will be successful, given that the full‐scale facility

will work, is 0.8. The probability that the pilot plant will fail, given that the full‐scale facility will fail, is 0.85. Calculate the posterior probabilities and reevaluate the decision tree from Problem 9.

Does this new information affect Diamond

Chemical’s original decisions?



Answer

10.• (a)

• (b) Build the pilot plant. If the pilot plant succeeds, build facility. If the pilot plant fails, don't build facility. Expected profit = $244,300.

•

Prior Probabilities P(Facility works) = 0.60

P(Facility fails) = 0.40

Conditional probabilities P(Pilot works | Facility works) = 0.80P(Pilot fails | Facility works) = 0.20

P(Pilot works | Facility fails) = 0.15P(Pilot fails | Facility fails) = 0.85

Posterior probabilities GIVEN pilot works Outcome P(Pilot works | Outcome) Prior prob Jt prob Post. prob

Facility works 0.80 0.60 0.48 0.89Facility fails 0.15 0.40 0.06 0.11

P(Pilot works) = 0.54Posterior probabilities GIVEN pilot fails

Outcome P(Pilot fails | Outcome) Prior prob Jt prob Post. probFacility works 0.20 0.60 0.12 0.26Facility fails 0.85 0.40 0.34 0.74

P(Pilot fails) = 0.46



Answer

10.



Question

11.• Shamrock Oil owns a parcel of land that has the potential to be an

underground oil field. It will cost $500,000 to drill for oil. If oil does

exist

on

the

land,

Shamrock

will

realize

a

payoff

of

$4,000,000

(not

including drilling costs). With current information, Shamrock estimates that there is a 0.2 probability that oil is present on the site. Shamrock also has the option of selling the land as is for $400,000, without further information about the likelihood of oil

being present. A third option is to perform geological tests at the site, which would cost $100,000. There is a 30% chance that the test results will be positive, after which Shamrock can sell the land

for $650,000 or drill the land, with a 0.65 probability that oil exists. If the test results are negative, Shamrock can sell the land for

$50,000 or drill the land, with 0.05 probability that oil exists. Using a decision tree, recommend a course of action for Shamrock Oil.



Answer

11.• Test the land. If the test result is positive, drill

for oil. If the test result is negative, sell the land. Expected profit = $565,000.

•

•



Answer

11.

Test land. If test is positive, drill. If test is negative, sell. Expected profit = $565,000.

Sell land

$400$400 $400

Sell land$550

0.3 $650 $550Positive2 0.65

$0 $2,000 Oil$3,400

Drill Land $4,000 $3,400

-$500 $2,000 0.35Test land Dry

-$600-$100 $565 $0 -$600

2$565 Sell land

-$500.7 $50 -$50

Negative1 0.05

$0 -$50 Oil$3,400

Drill land $4,000 $3,400

-$500 -$400 0.95

Dry-$600

$0 -$600

0.2Oil

$3,500Drill Land $4,000 $3,500

-$500 $300 0.8Dry

-$500

$0 -$500

Problem 11



Question

12.• Shamrock Oil (see Problem 11) has some revised

information concerning the accuracy of the geological test probabilities. According to this new information, the probability that the test will be positive, given that the oil is present in the

ground, is 0.85. The probability that the test will be negative, given that oil is not present, is 0.75. Calculate the posterior probabilities and

reevaluate the decision tree from problem 11.

Does this information affect Shamrock Oil’s original decision?



Answer

12.• (a)

• (b) Test the land. If the test result is positive, drill for oil. If the test result is negative, sell the land.

Expected profit = $427,300.

Prior Probabilities P(Oil well) = 0.20P(Dry well) = 0.80

Conditional probabilities P(Positive test | Oil well) = 0.85P(Negative test | Oil well) = 0.15P(Positive test | Dry well) = 0.25P(Negative test | Dry well) = 0.75

Posterior probabilities GIVEN positive test Outcome P(Positive test | Outcome) Prior prob Jt prob Post. prob

Oil well 0.85 0.20 0.17 0.46Dry well 0.25 0.80 0.20 0.54

P(Positive test) = 0.37

Posterior probabilities GIVEN negative test Outcome P(Negative test | Outcome) Prior prob Jt prob Post. prob

Oil well 0.15 0.20 0.03 0.05Dry well 0.75 0.80 0.60 0.95

P(Negative test) = 0.63



Answer

12.Test land. If test is positive, drill. If test is negative, sell. Expected profit = $427,300.

Sell land

$400$400 $400.00

Sell land$550

0.37 $650 $550Positive

2 0.46$0 $1,240 Oil

$3,400Drill Land $4,000 $3,400

-$500 $1,240 0.54Test land Dry

-$600-$100 $427.30 $0 -$600

2$427.30 Sell land

-$500.63 $50 -$50

Negative1 0.05

$0 -$50 Oil$3,400

Drill land $4,000 $3,400

-$500 -$400 0.95

Dry -$600$0 -$600

0.2Oil

$3,500Drill Land $4,000 $3,500

-$500 $300.00 0.8Dry

-$500

$0 -$500

Prob lem 12



Question

13• Shamrock Oil (see Problem 11) has decided to rely on utility theory to assist in the decision concerning the oil field. The following table describes its utility function; all monetary values

are in thousands of dollars:

• (a) Redo problem 11 using this information.

• (b) How can you best describe Shamrock Oil’s attitude toward

risk? Justify your answer.

Monetary Value ($) Utility

‐600 0.00

‐500 0.03

‐50 0.10

400 0.15

550 0.17

3400 0.90

3500 1.00



Answer

13.• (a) Test the land. If the test result is positive, drill for oil. If the

test result is negative, sell the land. Expected utility = 0.246.

•

•

Test land. If test is positive, drill. If test is negative, sell. Expected utility = 0.246.

Sell land

0.1500.150

Sell land

0.170

0.30 0.170

Positive

2 0.65

0.585 Oil

0.900

Drill Land 0.90

0.585 0.35

Test land Dry

0.000

0.246 0.00

2

0.246 Sell land

0.100

0.70 0.100

Negative

1 0.05

0.100 Oil

0.900

Drill land 0.90

0.045 0.95

Dry

0.000

0.00

0.20

Oil

1.000

Drill Land 1.000

0.224 0.80

Dry

0.030

0.030

Problem 13 (a)



Answer

13.• (b) Shamrock Oil is a risk seeker.

Dollar Utility

-$600 0.00

-$500 0.03

-$50 0.10

$400 0.15$550 0.17

$3,400 0.90

$3,500 1.00

Risk seeker.

Problem 13 (b)

0.00

0.25

0.50

0.75

1.00

-$600 $0 $600 $1,200 $1,800 $2,400 $3,000 $3,600

U t i l i t y

Monetary value

Utility Curve



Question 14.Jim Sellers is thinking about producing a new type of electric razor for men. If the market is good, he would get a return of $100,000, but if the market for this new type of razor is poor, he would lose $60,000. Because Ron Bush is a close friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested two options to Jim. The first alternative is a sophisticated questionnaire that would be administered to a test

market. It will cost $5,000. The second alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron has suggested that it would be a good idea for Jim to

conduct either the questionnaire or the pilot before making the decision concerning whether to produce the new razor. But Jim is not sure if the value of either option is

worth the cost.For the sake of solving this problem, assume that Jim has the following

probability estimates available: the probability of a successful market without performing the questionnaire or pilot study is 0.5, the probability of a successful market given a positive questionnaire result is 0.78, the probability of a successful market given a negative questionnaire result is 0.27, the probability of the successful market given a

positive pilot study result is 0.89, and the probability of a successful market given a negative pilot study result is 0.18. Further, the probability of a positive questionnaire result is 0.45 and the probability of a positive pilot study result is also 0.45.

(a) Draw the decision tree for this problem and identify the best decision for Jim.

(b) What is the value of the questionnaire’s information? What is its efficiency?

(c) What

is

the

value

of

the

pilot

study’s

information?

What

is

its

efficiency?



Answer

14.• (a)Conduct the survey questionnaire. If the

response is positive, produce razor. If the response is negative, do not produce razor. Expected return = $24,160.

•

• (b) EVPI = $30,000. EVSI = $9,160. Efficiency = 30.53%.

•

• (c) EVPI = $30,000. EVSI = $17,080. Efficiency = 56.93%.



Answer

14. 0.78

Good market(a) Conduct questionnaire. $95,000If positive, produce razor. Produce $1,00,000 $95,000

If negative, do not produce razor.Expected return = $24,160. $0 $59,800 0.22EVPI = $30,000 0.45 Poor market

Positive result -$65,000(b) EVSI = $9,160 1 -$60,000 -$65,000

Efficiency = 30.53% $0 $59,800

(c) EVSI = $17,080 Not ProduceEfficiency = 56.93% -$5,000

$0 -$5,000

Questionnaire0.27

-$5,000 $24,160 Good market$95,000

Produce $1,00,000 $95,000

$0 -$21,800 0.73

0.55 Poor marketNegative result -$65,000

2 -$60,000 -$65,000$0 -$5,000

Not Produce-$5,000

$0 -$5,000

0.89

Good market$80,000

Produce $1,00,000 $80,000

$0 $62,400 0.11

0.45 Poor marketPositive pilot -$80,000

1 -$60,000 -$80,000$0 $62,400

1 Not Produce$24,160 -$20,000

$0 -$20,000Pilot study

0.18

-$20,000 $17,080 Good market$80,000

Produce $1,00,000 $80,000

$0 -$51,200 0.820.55 Poor market

Negative pilot -$80,000

2 -$60,000 -$80,000$0 -$20,000

Not Produce-$20,000

$0 -$20,000

0.5Good market

$1,00,000

Produce $1,00,000 $1,00,000

$0 $20,000 0.5Poor market

Neither test -$60,000

1 -$60,000 -$60,000$0 $20,000

Not produce

$0$0 $0

Problem 14



Question

15.• Jim Sellers (see problem 14) has been able to

estimate

his

utility

for

a

number

of

different

values, and he would like to use these utility values in making his decision. The utility values are U (‐$80,000) = 0, U(‐$65,000) = 0.5, U(‐$60,000) = 0.55, U($80,000) = 0.9, U ($95,000) = 0.95, and U($100,000) = 1.

• (a) Solve Problem 14(a) again using utility values.

• (B) Is Jim a risk avoider or risk seeker? Justify your answer.



Answer

15.• (a) Conduct the survey questionnaire. If the survey response is positive,

produce razor. If the survey response is negative, do not produce razor.

Expected utility = 0.823.

•

0.78

Good market

Conduct questionnaire. 0.950

If positive, produce razor. Produce 0.950

If negative, do not produce razor.Expected utility = 0.823. 0.851 0.22

0.45 Poor market

Positive result 0.500

1 0.500

0.851

Not Produce

0.800

0.800

Questionnaire

0.27

0.823 Good market

0.950

Produce 0.950

0.622 0.73

0.55 Poor market

Negative result 0.500

2 0.500

0.800

Not Produce

0.800

0.800

0.89

Good market

0.900

Produce 0.900

0.801 0.11

0.45 Poor market

Positive pilot 0.000

1 0.000

0.00 0.801

1 Not Produce

0.823 0.700

0.700

Pilot study

0.18

0.745 Good market

0.900Produce 0.900

0.162 0.82

0.55 Poor market

Negative pilot 0.000

2 0.000

0.700

Not Produce

0.700

0.700

0.50

Good market

1.000

Produce 1.000

0.775 0.50

Poor market

Neither test 0.550

2 0.550

0.810

Not produce

0.810

0.810

Problem 15 (a)



Answer

15.• (b) Jim is a risk avoider.

Dollar Utility

-$80,000 0.00

-$65,000 0.50

-$20,000 0.70

-$5,000 0.80

$0 0.81

$80,000 0.90

$95,000 0.95

$1,00,000 1.00

Risk avoider.

Problem 15 (b)

0.00

0.25

0.50

0.75

1.00

-$80,000 -$40,000 $0 $40,000 $80,000

U t i l i t y

Monetary value

Utility Curve

Documents

Decision Analysis – Prac Prob 2015