CHAPTER 8

DECISION ANALYSIS

SOLUTIONS TO DISCUSSION QUESTIONS

8-1. The purpose of this question is to make students use a personal experience to distinguish between good and bad decisions. A good decision is based on logic and all of the available information. A bad decision is one that is not based on logic and the available information. It is possible for an unfortunate or undesirable outcome to occur after a good decision has been made. It is also possible to have a favorable or desirable outcome occur after a bad decision.

8-2. The decision-making process includes the following steps: (1) define the problem, (2) list the alternatives, (3) identify the possible outcomes, (4) evaluate the consequences, and (5) select an evaluation criterion and make the appropriate decision. The first four steps or procedures are common for all decision-making problems. Step 5, however, depends on the decision-making model used.

8-3. An alternative is a course of action over which we have complete control. A state of nature is an event or occurrence in which we have no control. An example of an alternative is deciding whether or not to take an umbrella to school or work on a particular day. An example of a state of nature is whether or not it will rain on a particular day.

8-4. The basic differences between decision-making models under certainty, risk, and uncertainty depend on the amount of chance or risk that is involved in the decision. A decision-making model under certainty assumes that we know with complete confidence the future outcomes. Decision-making-under-risk models assume that we do not know the outcomes for a particular decision but that we do know the probability of occurrence of those outcomes. With decision making under uncertainty, it is assumed that we do not know the outcomes that will occur, and furthermore, we do not know the probabilities that these outcomes will occur.

8-5. EMV is the expected monetary value. This is the expected return that we would realize if the decision were repeated an infinite number of times. EVwPI is the expected value with perfect information. This is the return or value of making the same decision an infinite number of times when we have perfect or complete information. EVPI is the expected value of perfect information. This is simply the difference between EMV and EVwPI. It is the amount that we would be willing to pay for perfect information.

8-6. A decision tree is preferred to a decision table when a number of sequential decisions are to be made. A sequential decision situation is one in which the outcome of one decision becomes an important factor in making future decisions. For example, if a decision maker is considering the possibility of acquiring additional information and a decision of whether or not to build a new plant, the decision to acquire the new information is made first. Then, based on the results of the new information (if it is gathered), the decision to build the plant is made. Therefore, these decisions are sequential. One is made before the other.

8-7. A prior probability is one that exists before additional information is gathered. A posterior probability is one that can be computed based on prior probabilities and additional information.

8-8. The purpose of Bayesian analysis is to determine posterior probabilities based on prior probabilities and new information. Bayesian analysis can be used in the decision-making process whenever additional information is gathered. This information can then be combined with prior probabilities in arriving at posterior probabilities. Once these posterior probabilities are computed, they can be used in the decision-making process as any other probability value.

8-9. The overall purpose of utility theory is to incorporate a decision maker’s preference for risk in the decision-making process.

8-10. A utility function can be assessed in a number of different ways. A common way is to use a standard gamble. With a standard gamble, the best outcome is assigned a utility of 1, and the worst outcome is assigned a utility of 0. Then, intermediate outcomes are selected and the decision maker is given a choice between having the intermediate outcome for sure and a gamble involving the best and worst outcomes. The probability that makes the decision maker indifferent between having the intermediate outcome for sure and a gamble involving the best and worst outcomes is determined. This probability then becomes the utility of the intermediate value. This process is continued until utility values for all economic consequences are determined. These utility values are then placed on a utility curve.

8-11. When a utility curve is to be used in the decision-making process, utility values from the utility curve replace all monetary values at the terminal branches in a decision tree or in the body of a decision table. Then, expected utilities are determined in the same way as expected monetary values. The alternative with the highest expected utility is selected as the best decision.

8-12. A risk seeker is a decision maker who enjoys and seeks out risk. A risk avoider is a decision maker who avoids risk even if the economic payoff is higher. The utility curve for a risk seeker increases at an increasing rate. The utility curve for a risk avoider increases at a decreasing rate.

SOLUTIONS TO PROBLEMS

8-13. See file P8-13.XLS.Outcomes (a) Maximax (b) Maximin (c) EMV

Alternatives Fav mkt Unfav mkt Maximum Choice Minimum Choice EMV ChoiceSub 100 $300,000 -$200,000 $300,000 Best -$200,000 $150,000 BestOiler J $250,000 -$100,000 $250,000 -$100,000 $145,000Texan $75,000 -$18,000 $75,000 -$18,000 Best $47,100

8-14. See file P8-14.XLS.(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.6)

Alternatives Maximum Choice Minimum Choice Average Choice Realism ChoiceExpand $56,000 -$29,000 $16,000 $22,000Move $70,000 Best -$45,000 $20,000 Best $24,000 BestNo change $30,000 $5,000 Best $15,000 $20,000

Regret Outcomes (e) MinimaxAlternatives Good Average Poor Maximum ChoiceExpand $14,000 $14,000 $34,000 $34,000 BestMove $0 $0 $50,000 $50,000No change $40,000 $25,000 $0 $40,000

8-15. See file P8-15.XLS.Alternatives EMV ChoiceExpand $14,750Move $19,750 BestNo change $13,500

Expected Value WITH Perfect Information (EVwPI) = $34,750Best Expected Monetary Value (EMV) = $19,750Expected Value OF Perfect Information (EVPI) = $15,000

Alternatives EOL ChoiceExpand $20,000Move $15,000 BestNo change $21,250

8-16. See file P8-16.XLS.(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.5) (e) Minimax

Alternatives Maximum Choice Minimum Choice Average Choice Realism Choice Maximum ChoiceStocks 12% Best -10% 3% 1% 12%Bonds 7% 1% 4% Best 4% Best 5% BestMoney Mkt 4% 2% Best 3% 3% 8%

8-17. See file P8-17.XLS.Alternatives EMV ChoiceStocks 0.00%Bonds 3.25% BestMoney Market 2.75%

Expected Value WITH Perfect Information (EVwPI) = 5.40%Best Expected Monetary Value (EMV) = 3.25%Expected Value OF Perfect Information (EVPI) = 2.15%

Alternatives EOL ChoiceStocks 5.40%Bonds 2.15% BestMoney Market 2.65%

8-18. See file P8-18.XLS.(a) Outcomes (b) Equally Likely (c) Hurwicz (0.75)

Alternatives Grow Same Average Choice Realism ChoiceLarge wing $150,000 -$85,000 $32,500 Best $91,250 BestSmall wing $60,000 -$45,000 $7,500 $33,750No wing $0 $0 $0 $0

8-19. See file P8-19.XLS.(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.4) (e) Minimax

Alternatives Maximum Choice Minimum Choice Average Choice Realism Choice Maximum Choice100 $75 $75 Best $75 $75 Best $150200 $150 -$50 $83 Best $30 $125 Best300 $225 Best -$175 $25 -$15 $250

8-20. See file P8-20.XLS.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 $69

300 $144

8-21. See file P8-21.XLS.(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.7) (e) Minimax

Alternatives Maximum Choice Minimum Choice Average Choice Realism Choice Maximum Choice50 $500 $500 Best $500 $500 $1,500100 $1,000 -$300 $675 Best $610 $1,000 Best150 $1,500 -$1,100 $525 $720 $1,600200 $2,000 Best -$1,900 $50 $830 Best $2,400

8-22. See file P8-22.XLS.

Alternatives EMV Choice50 $500100 $740 Best150 $525200 -$15

Expected Value WITH Perfect Information (EVwPI) = $1,225Best Expected Monetary Value (EMV) = $740Expected Value OF Perfect Information (EVPI) = $485

Alternatives EOL Choice50 $725100 $485 Best150 $700200 $1,240

8-23. See file P8-23.XLS.Outcomes

Alternatives 6 7 8 9 EMV Choice6 $300 $300 $300 $300 $300.007 $255 $350 $350 $350 $340.508 $210 $305 $400 $400 $352.50 Best9 $165 $260 $355 $450 $317.00Probability 0.1 0.3 0.5 0.1

8-24. See file P8-24.XLS.(a) Maximax (b) Maximin (c) Equally Likely (d) Hurwicz (0.8) (e) Minimax

Alternatives Maximum Choice Minimum Choice Average Choice Realism Choice Maximum ChoiceSmall $50,000 -$10,000 Best $20,000 $38,000 $250,000Medium $80,000 -$20,000 $30,000 $60,000 $220,000

Large $100,000 -$40,000 $30,000 $72,000 $200,000Very large $300,000 Best -$160,000 $55,000 Best $208,000 Best $150,000 Best

8-25. See file P8-25.XLS. Note: In this problem, lower times are the preferred outcome. Therefore we select the alternative with the lowest EMV. Calculate regret as (time taken - best time taken), then select alternative with lowest EOL. EVPI = Best EMV – EVwPI. Alternatively, we can multiply all payoffs by -1, and solve this problem like any other problem.

PAYOFFS OutcomesAlternatives None Mild Severe EMV ChoiceTennessee 15 30 45 25.00Back roads 20 25 35 24.17 BestExpressway 30 30 30 30.00

Best Expected Time (EMV) = 24.17Expected Value WITH Perfect Information (EVwPI) = 20.83Expected Value OF Perfect Information (EVPI) = 3.33

REGRET OutcomesAlternatives None Mild Severe EOL ChoiceTennessee 0 5 15 4.17Back roads 5 0 5 3.33 BestExpressway 15 5 0 9.17

8-26.(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) See file P8-26.XLS for the TreePlan solution. Conduct study. 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%.

8-27.(a) See file P8-27.XLS, sheet (a) for the utility curve. They are risk avoiders.

(b) See file P8-27.XLS, sheet (a) for the Tree Plan solution. Expected utility if we conduct the survey = 0.761. Expected utility if we do not conduct the survey = 0.90. Therefore, the medical professionals should not conduct the survey, and should not construct the clinic.

8-28. See file P8-28.XLS for Tree Plan solution.

(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%.

8-29. See file P8-29.XLS for the TreePlan solution. Note: All costs have been expressed as negative amounts in the decision tree. Hence, we select highest expected values at all nodes.(a) Use supplier A. Expected cost is $90 with supplier A versus $113 with supplier B. Note: In the tree, we pick the EMV of -$90 over the EMV of -$113.

(b) $37 + ($113 - $90) = $60 less than supplier A.

8-30. See file P8-30.XLS for the TreePlan solution.Market the new golf balls. If competitor enters market, set price Medium. If competitor does not enter market, set the price High. EMV = $325,000.

8-31. See file P8-31.XLS for the TreePlan solution.Hire Samantha Adams. If she says cold, Ajay should buy a new blower. If she says not cold, Ajay should repair the old blower. Expected profit = $176.88. EVSI = $101.88. EVwPI = $340.00. Maximum EMV = $125.00. EVPI = $215.00. Efficiency = 47.38%.

8-32. See file P8-32.XLS for the TreePlan solution.(a) Hire Susan. If she says good chance of being sunny, take lemonade. If she says bad chance of being sunny, take cocoa. Expected profit = $50.36.

(b) EVSI = $10.36

8-33. See file P8-33.XLS for the TreePlan solution.Build the pilot plant. If the pilot plant succeeds, build facility. If the pilot plant fails, don't build facility. Expected profit = $209,500.

8-34.(a)

Prior ProbabilitiesP(Facility works) = 0.60P(Facility fails) = 0.40

Conditional probabilitiesP(Pilot works | Facility works) = 0.80P(Pilot fails | Facility works) = 0.20P(Pilot works | Facility fails) = 0.15P(Pilot fails | Facility fails) = 0.85

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

Facility works 0.80 0.60 0.48 0.89

Facility fails 0.15 0.40 0.06 0.11P(Pilot works) = 0.54

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

Facility works 0.20 0.60 0.12 0.26Facility fails 0.85 0.40 0.34 0.74

P(Pilot fails) = 0.46

(b) See file P8-34.XLS for the revised TreePlan solution. Build the pilot plant. If the pilot plant succeeds, build facility. If the pilot plant fails, don't build facility. Expected profit = $244,300.

8-35. See file P8-35.XLS for the TreePlan solution. Accept the wager. Use a hard first serve. If the first serve is out of play, use a hard second serve. Expected payoff = $17.60.

8-36.(a) See file P8-36.XLS, sheet (a) for the TreePlan solution. Accept the wager. Use a hard first serve. If the first serve is out of play, use a hard second serve. Expected utility = 0.588.

(b) See file P8-36.XLS, sheet (b) for the utility curve. You are a risk avoider.

8-37. See file P8-37.XLS for the TreePlan solution.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.

8-38.(a)

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

Conditional probabilitiesP(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 testOutcome 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) = 0.37Posterior probabilities GIVEN negative test

Outcome P(Negative test | Outcome) Prior prob Jt prob Post. probOil well 0.15 0.20 0.03 0.05Dry well 0.75 0.80 0.60 0.95

P(Negative test) = 0.63

(b) See file P8-38.XLS for the TreePlan solution.

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.

8-39.(a) See file P8-39.XLS, sheet (a) for the TreePlan solution. 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.

(b) See file P8-39.XLS, sheet (b) for the utility curve. Shamrock Oil is a risk seeker.

8-40.(a) See file P8-40.XLS for the TreePlan solution. 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%.

8-41.(a) See file P8-41.XLS, sheet (a) for the TreePlan solution. 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.

(b) See file P8-41.XLS, sheet (b) for the utility curve. Jim is a risk avoider.

8-42. See file P8-42.XLS for the TreePlan solution.Don't lock-in now. If the rate increases after one month, lock-in then. If the rate is unchanged or decreases after one month, don't lock-in and accept current rate at settlement. Expected cost = $270.

8-43.(a) See file P8-43.XLS, sheet (a) for the utility curve. Jason is a risk seeker.

(b) See file P8-43.XLS, sheet (b) for the TreePlan solution. The use of utilities does not affect Jason’s decision. The recommended course is still to not lock-in now. If the rate increases after one month, lock-in then. If the rate is unchanged or decreases after one month, don't lock-in and accept current rate at settlement. Expected utility = 0.261.

8-44. See file P8-44.XLS for the TreePlan solution.(a) Get the information. If it is favorable, build the store. If it is unfavorable, don't build the store. Expected return = $29,200.

(b) EVPI = $32,000. EVSI = $21,200. Efficiency = 66.25%.

8-45.

(a) See file P8-45.XLS, sheet (a) for the TreePlan solution. Get the information. If it is favorable, build the store. If it is unfavorable, don't build the store. Expected utility = 0.62.(b) See file P8-45.XLS, sheet (b) for the utility curve. Sue is a risk seeker.

8-46. See file P8-46.XLS for the TreePlan solution.If the survey is not conducted, the medium facility, with an EMV of $670,000, is selected. If the survey is conducted, we first compute the revised probabilities using Bayes’ theorem, as follows.

Prior ProbabilitiesP(Low demand) = 0.15P(Fair demand) = 0.40P(High demand) = 0.45

Conditional probabilitiesP(Low survey | Low demand) = 0.70P(Fair survey | Low demand) = 0.20P(High survey | Low demand) = 0.10P(Low survey | Fair demand) = 0.40P(Fair survey | Fair demand) = 0.50P(High survey | Fair demand) = 0.10P(Low survey | High demand) = 0.10P(Fair survey | High demand) = 0.30P(High survey | High demand) = 0.60

Posterior probabilities GIVEN low surveyOutcome P(Low survey | Outcome) Prior prob Jt prob Post. prob

Low demand 0.70 0.15 0.105 0.339Fair demand 0.40 0.40 0.160 0.516High demand 0.10 0.45 0.045 0.145

P(Low survey) = 0.310Posterior probabilities GIVEN fair survey

Outcome P(Fair survey | Outcome) Prior prob Jt prob Post. probLow demand 0.20 0.15 0.030 0.082Fair demand 0.50 0.40 0.200 0.548High demand 0.30 0.45 0.135 0.370

P(Fair survey) = 0.365Posterior probabilities GIVEN high survey

Outcome P(High survey | Outcome) Prior prob Jt prob Post. probLow demand 0.10 0.15 0.015 0.046Fair demand 0.10 0.40 0.040 0.123High demand 0.60 0.45 0.270 0.831

P(High survey) = 0.325

If the survey results are low, the best decision is to build the medium facility with an EMV of $495,000. If the survey results are medium, the best decision is also to build the medium plant with an EMV of $646,000. Finally, if the survey results are high, the best decision is to build the large facility with an EMV of $821,000. Now, we can take these results and multiply them times the probability of having low survey results, medium survey results, and high survey results to get the expected value of taking the survey and selecting the appropriate decision. The resulting EMV is approximately $656,000. Because

the EMV for not conducting the survey is greater ($670,000), the best decision is to not conduct the survey and to build the medium-sized facility.

8-47. See file P8-47.XLS.(a) Posterior probabilities GIVEN favorable surveyOutcome P(Favorable | Outcome) Prior prob Jt prob Post. probSuccess 0.80 0.50 0.400 0.727Failure 0.30 0.50 0.150 0.273

P(Favorable survey) = 0.550(b) Posterior probabilities GIVEN unfavorable surveyOutcome P(Unfavorable | Outcome) Prior prob Jt prob Post. probSuccess 0.20 0.50 0.100 0.222Failure 0.70 0.50 0.350 0.778

P(Unfavorable survey) = 0.450

8-48. See file P8-48.XLS.Posterior probabilities GIVEN favorable survey

Outcome P(Favorable | Outcome) Prior prob Jt prob Post. probFav market 0.875 0.550 0.481 0.855Unfav market 0.182 0.450 0.082 0.145

P(Favorable survey) = 0.563Posterior probabilities GIVEN unfavorable survey

Outcome P(Favorable | Outcome) Prior prob Jt prob Post. ProbFav market 0.125 0.550 0.069 0.157Unfav market 0.818 0.450 0.368 0.843

P(Unfavorable survey) = 0.437

8-49. See file P8-49.XLS.Posterior probabilities GIVEN growth predictionOutcome P(Growth predn | Outcome) Prior prob Jt prob Post. probActual growth 0.75 0.30 0.225 0.696Actual steady 0.18 0.45 0.081 0.250Actual decline 0.07 0.25 0.018 0.054

P(Growth prediction) = 0.324Posterior probabilities GIVEN steady predictionOutcome P(Steady predn | Outcome) Prior prob Jt prob Post. probActual growth 0.08 0.30 0.024 0.058Actual steady 0.80 0.45 0.360 0.870Actual decline 0.12 0.25 0.030 0.072

P(Steady prediction) = 0.414Posterior probabilities GIVEN decline predictionOutcome P(Decline predn | Outcome) Prior prob Jt prob Post. probActual growth 0.05 0.30 0.015 0.054Actual steady 0.12 0.45 0.054 0.195Actual decline 0.83 0.25 0.208 0.750

P(Decline prediction) = 0.277

8-50.(a) See file P8-50.XLS, sheet (a). Travel time on expressway = 30 minutes. Expected travel time on Broad Street = (40)(0.5) + (15)(0.5) = 27.5 minutes. Use Broad Street.(b) See file P8-50.XLS, sheet (b). Utility of travel time on expressway = 0.7. Expected utility on Broad Street = (0.2)(0.5) + (0.9)(0.5) = 0.55. The expressway maximizes utility.(c) See file P8-50.XLS, sheet (c) for the utility curve. Lynn is a risk avoider.

Case: Ski Right

(1) See file P8-Ski.XLS. The best decision is to have Leadville Barts make the helmets and have Progressive Products make the rest. Expected value = $2,600. The option of not using Progressive was, however, very close with an expected value of $2,500.

PAYOFFS OutcomesAlternatives Poor Average Good Excellent EMV ChoicePP -$5,000 -$2,000 $2,000 $5,000 $700LB and PP -$10,000 -$4,000 $6,000 $12,000 $2,600 BestTR and PP -$15,000 -$10,000 $7,000 $13,000 $900CC and PP -$30,000 -$20,000 $10,000 $30,000 $1,000LB, CC, and TR -$60,000 -$35,000 $20,000 $55,000 $2,500Probability 0.1 0.3 0.4 0.2

(2 and 3) The opportunity loss and EVPI computations are as follows.

Expected Value WITH Perfect Information (EVwPI) = $17,900Best Expected Monetary Value (EMV) = $2,600Expected Value OF Perfect Information (EVPI) = $15,300

REGRET Outcomes

Alternatives Poor Average Good Excellent EOL ChoicePP $0 $0 $18,000 $50,000 $17,200LB and PP $5,000 $2,000 $14,000 $43,000 $15,300 BestTR and PP $10,000 $8,000 $13,000 $42,000 $17,000CC and PP $25,000 $18,000 $10,000 $25,000 $16,900LB, CC, and TR $55,000 $33,000 $0 $0 $15,400Probability 0.1 0.3 0.4 0.2

(4) Clearly, there are a number of options that Bob did not consider.

Case: Blake Electronics

(1) MAI’s proposal directly gives Steve the conditional probabilities he needs (e.g., probability of a successful venture given a favorable survey). Although the information from Iverstine and Kinard (I&K) is different, we can easily use Bayes’ theorem to on I&K information to compute the revised probabilities (see file P8-Blake.XLS, sheet Posterior). As such, does not need any additional information from I&K.

(2) Steve’s problem involves three decisions. First, should he contract the services of an outside research agency? Second, if a survey is warranted, should he employ MAI or I&K? Third, in any case, should the new product line be introduced?

The TreePlan solution for Steve’s problem is shown in file P8-Blake.XLS.

If Steve decides not to conduct a survey, the decision is to introduce the product with an EMV of $700,000 [= (0.6)($1,500,000) + (0.4)(-$500,000)].

If Steve decides to conduct the survey, he has to choose between MAI and I&K. If he chooses MAI for the survey, the best choice is to introduce the product irrespective of whether the survey results are favorable or unfavorable. The EMV is $800,000 if the survey results are favorable, while the EMV is only $200,000 if the survey results are unfavorable. The overall EMV of hiring MAI is $500,000 [= (0.5)($800,000) + (0.5)($200,000)].

If Steve chooses I&K for the survey, the best choice is to introduce the product if survey results are favorable, for an EMV of $940,000. On the other hand, if the survey results are unfavorable, the best decision is to not introduce the product for an EMV of -$300,000 (the cost of the survey). The overall EMV of hiring MAI is $468,800 [= (0.62)($940,000) + (0.38)(-$300,000)].

Comparing these alternatives, Steve should not hire either firm to do the survey. He should simply choose to introduce the produce right away for an EMV of $700,000.