# Introduction to Management Science Study Set 3

## Quiz 12 :Decision Analysis

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A farmer in Iowa is considering either leasing some extra land or investing in savings certificates at the local bank. If weather conditions are good next year, the extra land will give the farmer an excellent harvest. However, if weather conditions are bad, the farmer will lose money. The savings certificates will result in the same return, regardless of the weather conditions. The return for each investment, given each type of weather condition, is shown in the following payoff table: Select the best decision, using the following decision criteria: a. Maximax b. Maximin
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Maximax Criterion - Select the maximum payoff for each decision. Then, select the maximum of those maximum payoffs.
Maximin Criterion - Select the minimum payoff for each decision. Then, select the maximum of those minimum payoffs.
Consider the following information as shown below:
a.
Calculate the maximum cost decision by using the following formulas in the excel as shown below:
Following values will be obtained:
Therefore, the best decision using the maxi-max approach is lease land.
b.
Calculate the maximum of minimum cost decision by using the following formulas in the excel as shown below:
Following values will be obtained:
Therefore, the best decision using the maximin approach is buy saving certificate.

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The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company's equipment to another company. The profit that will result from each alternative will be determined by whether material costs remain stable or increase. The profit from each alternative, given the two possibilities for material costs, is shown in the following payoff table: Determine the best decision, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz ( =.2) e. Equal likelihood
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Maximax Criterion - Select the maximum payoff for each decision. Then, select the maximum of those maximum payoffs.
Maximin Criterion - Select the minimum payoff for each decision. Then, select the maximum of those minimum payoffs.
a.
Excel can be used to identify the maximum payoff for each decision. First set up the excel file as shown below. Next, enter the amount of profit for each decision if the material cost is stable or increased. Enter the formula =Max(C5,D5) into cell E5. Copy this formula into E6 and E7. This formula finds the maximum payoff for each decision. Lastly, enter the formula =Max(E5:E7) into cell C9 to find the maximum of the maximum payoffs. The result is $105,000 which means the Maximax decision is to build a shopping center. b. To find the minimum payoff for each decision, enter =Min(C5,D5) into cell F5. Copy this formula into cells F6 and F7. Enter the formula =Max(F5:F7) into cell C10 to find the maximum of the minimum payoffs. The result is$40,000 which means the Maximin decision is to lease the company's equipment.
Minimax Regret Criterion - The goal is to select the decision with the least regret. Select the maximum payoff under each condition. Then, subtract the payoff from each decision from this selected payoff under each condition. A regret table can help to identify the maximum regret for each decision. Choose the decision with the minimum regret.
c.
Enter the formula =MAX(C$5:C$7)-C5 into cell C15. Then, copy this formula into all the cells of the regret table. These formulas select the maximum payoff if the material cost is stable or increased and subtracts from it the profit from under each decision. The result is the following excel spreadsheet.
Next, enter the formula =Max(C15,D15) into cell E15. Copy this formula into E16 and E17. This formula finds the maximum regret for each decision.
Lastly, enter the formula =MIN(E15:E17) into cell D19 to find the minimum amount of regret out of the decisions. The result is $20,000 which means the minimax regret decision is to construct a shopping center. d. Hurwicz Criterion - For each decision, multiply the coefficient of optimism, , by the maximum payoff, and multiply the coefficient of pessimism, , by the minimum payoff. Add these products. Choose the maximum weighted payoffs determined for each decision. The given coefficient of optimism is 0.20 which means the coefficient of pessimism is . Multiply 0.20 by the maximum payoff for the decision of building houses and multiply 0.80 by the minimum payoff for the decision of building houses. This results in the formula =C5*C22+D5*C23 in cell C24 in the excel spreadsheet below. Under the same reasoning, cell C25 contains the formula =C6*C22+D6*C23, and cell C26 contains the formula =C7*C22+D7*C23. Choose the decision with the maximum weighted payoff. Since$40,000 is the greatest profit, the Hurwicz Criterion results in planting leasing the company's equipment.
e.
Equal Likelihood Criterion - Weight each state of nature equally. Multiply the payoffs for each decision by this equal weight and add the product. Choose the decision with the maximum weighted payoff.
There are two states of nature in this problem: bill passing or not passing. So, each state of nature is weighted equally, 0.50. Multiply the payoffs under each state of nature for each decision by 0.50 and add the product. Enter the formula =C5*C29+D5*C29 into cell C30, enter the formula =C6*C29+D6*C29 into cell C31, and enter =C7*C29+D7*C29 into cell C32.
Choose the decision with the maximum weighted payoff. Since $62,500 is the greatest profit, the Equal Likelihood Criterion results in constructing a shopping center. Tags Choose question tag The Tech football coaching staff has six basic offensive plays it runs every game. Tech has an upcoming game against State on Saturday, and the Tech coaches know that State employs five different defenses. The coaches have estimated the number of yards Tech will gain with each play against each defense, as shown in the following payoff table: a. If the coaches employ an offensive game plan, they will use the maximax criterion. What will be their best play b. If the coaches employ a defensive plan, they will use the maximin criterion. What will be their best play c. What will be their best offensive play if State is equally likely to use any of its five defenses Free Essay Answer: Answer: Maximax Criterion - Select the maximum payoff for each decision. Then, select the maximum of those maximum payoffs. Maximin Criterion - Select the minimum payoff for each decision. Then, select the maximum of those minimum payoffs. a. Excel can be used to identify the maximum payoff for each decision. First set up the excel file as shown below. Next, enter the number of yards the team will gain for a play based on the difference defenses the other team will run. Enter the formula =Max(C5:G5) into cell H5. Copy this formula into H6, H7, H8, H9, and H10. This formula finds the maximum number of yards for each play. Enter the formula =Max(H5:H10) into cell C12 to find the maximum of the maximum payoffs. The result is 20 yards which means the Maximax decision is run a Pass. b. To find the minimum payoff for each decision, enter =Min(C5:G5) into cell I5. Copy this formula into cells I6, I7, I8, I9, and I10. Enter the formula =Max(I5:I10) into cell C13 to find the maximum of the minimum payoffs. The result is losing 2 yards which means the Maximin decision is to run either Off Tackle or Option. c. Equal Likelihood Criterion - Weight each state of nature equally. Multiply the payoffs for each decision by this equal weight and add the product. Choose the decision with the maximum weighted payoff. There are five states of nature in this problem. So, each state of nature is weighted equally, . Multiply the number of yards under each state of nature by 0.20 and add the product for each play. Enter the formula =C5*C16+D5*C16+E5*C16+F5*C16+G5*C16 into cell C17, enter the formula =C6*C16+D6*C16+E6*C16+F6*C16+G6*C16 into cell C18, enter the formula =C7*C16+D7*C16+E7*C16+F7*C16+G7*C16 into cell C19, enter the formula =C8*C16+D8*C16+E8*C16+F8*C16+G8*C16 into cell C20, enter the formula =C9*C16+D9*C16+E9*C16+F9*C16+G9*C16 into cell C21, and enter the formula =C10*C16+D10*C16+E10*C16+F10*C16+G10*C16 into cell C22. Choose the decision with the maximum weighted payoff. Since 6.8 is the highest weighted number of yards of all the plays, the Equal Likelihood Criterion results in running a Toss Sweep. Tags Choose question tag Brooke Bentley, a student in business administration, is trying to decide which management science course to take next quarter-I, II, or III. "Steamboat" Fulton, "Death" Ray, and "Sadistic" Scott are the three management science professors who teach the courses. Brooke does not know who will teach what course. Brooke can expect a different grade in each of the courses, depending on who teaches it next quarter, as shown in the following payoff table: Determine the best course to take next quarter, using the following criteria. a. Maximax b. Maximin Essay Answer: Tags Choose question tag A company must decide now which of three products to make next year to plan and order proper materials. The cost per unit of producing each product will be determined by whether a new union labor contract passes or fails. The cost per unit for each product, given each contract result, is shown in the following payoff table: Determine which product should be produced, using the following decision criteria. a. Minimin b. Minimax Essay Answer: Tags Choose question tag A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and the probabilities associated with each contract outcome are shown in the following payoff table: Compute the expected value for each purchase and select the best one. Essay Answer: Tags Choose question tag A television network is attempting to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama versus Auburn, Georgia versus Georgia Tech, or Army versus Navy. The estimated viewer ratings (millions of homes) for the games depend on the win-loss records of the six teams, as shown in the following payoff table: Determine the best game to televise, using the following decision criteria. a. Maximax b. Maximin c. Equal likelihood Essay Answer: Tags Choose question tag Place-Plus, a real estate development firm, is considering several alternative development projects. These include building and leasing an office park, purchasing a parcel of land and building an office building to rent, buying and leasing a warehouse, building a strip mall, and building and selling condominiums. The financial success of these projects depends on interest rate movement in the next 5 years. The various development projects and their 5-year financial return (in$1,000,000s), given that interest rates will decline, remain stable, or increase, are shown in the following payoff table: Determine the best investment, using the following decision criteria. a. Maximax b. Maximin c. Equal likelihood d. Hurwicz ( =.3)
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Steeley Associates, Inc., a property development firm, purchased an old house near the town square in Concord Falls, where State University is located. The old house was built in the mid-1800s, and Steeley Associates restored it. For almost a decade, Steeley has leased it to the university for academic office space. The house is located on a wide lawn and has become a town landmark. However, in 2008, the lease with the university expired, and Steeley Associates decided to build high-density student apartments on the site, using all the open space. The community was outraged and objected to the town council. The legal counsel for the town spoke with a representative from Steeley and hinted that if Steeley requested a permit, the town would probably reject it. Steeley had reviewed the town building code and felt confident that its plan was within the guidelines, but that did not necessarily mean that it could win a lawsuit against the town to force the town to grant a permit. The principals at Steeley Associates held a series of meetings to review their alternatives. They decided that they had three options: They could request the permit, they could sell the property, or they could request a permit for a low-density office building, which the town had indicated it would not fight. Regarding the last two options, if Steeley sells the house and property, it thinks it can get $900,000. If it builds a new office building, its return will depend on town business growth in the future. It feels that there is a 70% chance of future growth, in which case Steeley will see a return of$1.3 million (over a 10-year planning horizon); if no growth (or erosion) occurs, it will make only $200,000. If Steeley requests a permit for the apartments, a host of good and bad outcomes are possible. The immediate good outcome is approval of its permit, which it estimates will result in a return of$3 million. However, Steeley gives that result only a 10% chance that it will occur. Alternatively, Steeley thinks there is a 90% chance that the town will reject its application, which will result in another set of decisions. Steeley can sell the property at that point. However, the rejection of the permit will undoubtedly decrease the value to potential buyers, and Steeley estimates that it will get only $700,000. Alternatively, it can construct the office building and face the same potential outcomes it did earlier, namely, a 30% chance of no town growth and a$200,000 return or a 70% chance of growth with a return of $1.3 million. A third option is to sue the town. On the surface, Steeley's case looks good, but the town building code is vague, and a sympathetic judge could throw out its suit. Whether or not it wins, Steeley estimates its possible legal fees to be$300,000, and it feels it has only a 40% chance of winning. However, if Steeley does win, it estimates that the award will be approximately $1 million, and it will also get its$3 million return for building the apartments. Steeley also estimates that there is a 10% chance that the suit could linger on in the courts for such a long time that any future return would be negated during its planning horizon, and it would incur an additional $200,000 in legal fees. If Steeley loses the suit, it will then be faced with the same options of selling the property or constructing an office building. However, if the suit is carried this far into the future, it feels that the selling price it can ask will be somewhat dependent on the town's growth prospects at that time, which it feels it can estimate at only 50-50. If the town is in a growth mode that far in the future, Steeley thinks that$900,000 is a conservative estimate of the potential sale price, whereas if the town is not growing, it thinks $500,000 is a more likely estimate. Finally, if Steeley constructs the office building, it feels that the chance of town growth is 50%, in which case the return will be only$1.2 million. If no growth occurs, it conservatively estimates only a $100,000 return. A. Perform a decision tree analysis of Steeley Associates's decision situation, using expected value, and indicate the appropriate decision with these criteria. B. Indicate the decision you would make and explain your reasons. Essay Answer: Tags Choose question tag Stevie Stone, a bellhop at the Royal Sundown Hotel in Atlanta, has been offered a management position. Although accepting the offer would assure him a job if there was a recession, if good economic conditions prevailed, he would actually make less money as a manager than as a bellhop (because of the large tips he gets as a bellhop). His salary during the next 5 years for each job, given each future economic condition, is shown in the following payoff table: Select the best decision, using the following decision criteria. a. Minimax regret b. Hurwicz ( =.4) c. Equal likelihood Essay Answer: Tags Choose question tag Microcomp is a U.S.-based manufacturer of personal computers. It is planning to build a new manufacturing and distribution facility in either South Korea, China, Taiwan, the Philippines, or Mexico. It will take approximately 5 years to build the necessary infrastructure (e.g., roads), construct the new facility, and put it into operation. The eventual cost of the facility will differ between countries and will even vary within countries depending on the financial, labor, and political climate, including monetary exchange rates. The company has estimated the facility cost (in$1,000,000s) in each country under three different future economic and political climates, as follows: Determine the best decision, using the following decision criteria. a. Minimin b. Minimax c. Hurwicz ( =.4) d. Equal likelihood
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WestCom Systems Products Company develops computer systems and software products for commercial sale. Each year it considers and evaluates a number of different R D projects to undertake. It develops a road map for each project, in the form of a standardized decision tree that identifies the different decision points in the R D process from the initial decision to invest in a project's development through the actual commercialization of the final product. The first decision point in the R D process is whether to fund a proposed project for 1 year. If the decision is no, then there is no resulting cost; if the decision is yes, then the project proceeds at an incremental cost to the company. The company establishes specific short-term, early technical milestones for its projects after 1 year. If the early milestones are achieved, the project proceeds to the next phase of project development; if the milestones are not achieved, the project is abandoned. In its planning process, the company develops probability estimates of achieving and not achieving the early milestones. If the early milestones are achieved, the project is funded for further development during an extended time frame specific to a project. At the end of this time frame, a project is evaluated according to a second set of (later) technical milestones. Again, the company attaches probability estimates for achieving and not achieving these later milestones. If the later milestones are not achieved, the project is abandoned. If the later milestones are achieved, technical uncertainties and problems have been overcome, and the company next assesses the project's ability to meet its strategic business objectives. At this stage, the company wants to know if the eventual product coincides with the company's competencies and whether there appears to be an eventual, clear market for the product. It invests in a product "prelaunch" to ascertain the answers to these questions. The outcomes of the prelaunch are that either there is a strategic fit or there is not, and the company assigns probability estimates to each of these two possible outcomes. If there is not a strategic fit at this point, the project is abandoned and the company loses its investment in the prelaunch process. If it is determined that there is a strategic fit, then three possible decisions result: (1) The company can invest in the product's launch, and a successful or unsuccessful outcome will result, each with an estimated probability of occurrence; (2) the company can delay the product's launch and at a later date decide whether to launch or abandon; and (3) if it launches later, the outcomes are success or failure, each with an estimated probability of occurrence. Also, if the product launch is delayed, there is always a likelihood that the technology will become obsolete or dated in the near future, which tends to reduce the expected return. The following table provides the various costs, event probabilities, and investment outcomes for five projects the company is considering: Determine the expected value for each project and then rank the projects accordingly for the company to consider.
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Ann Tyler has come into an inheritance from her grandparents. She is attempting to decide among several investment alternatives. The return after 1 year is primarily dependent on the interest rate during the next year. The rate is currently 7%, and Ann anticipates that it will stay the same or go up or down by at most two points. The various investment alternatives plus their returns ($10,000s), given the interest rate changes, are shown in the following table: Determine the best investment, using the following decision criteria. a. Maximax b. Maximin c. Equal likelihood Essay Answer: Tags Choose question tag A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each crop, given the two possible results on the trade bill, is shown in the following payoff table: Determine the best crop to plant, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz ( =.3) Essay Answer: Tags Choose question tag The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the playoffs next season. The team is considering four players: Barry Byrd, Rayneal O'Neil, Marvin Johnson, and Michael Gordan. Each player differs according to position, ability, and attractiveness to fans. The payoffs (in$1,000,000s) to the team for each player, based on the contract, profits from attendance, and team product sales for several different season outcomes, are provided in the following table: Determine the best decision, using the following decision criteria. a. Maximax b. Maximin c. Hurwicz ( =.60) d. Equal likelihood
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A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment: Determine the best investment, using the following decision criteria. a. Maximax b. Maximin c. Minimax regret d. Hurwicz ( =.4) e. Equal likelihood
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The Carolina Cougars is a major league baseball expansion team beginning its third year of operation. The team had losing records in each of its first 2 years and finished near the bottom of its division. However, the team was young and generally competitive. The team's general manager, Frank Lane, and manager, Biff Diamond, believe that with a few additional good players, the Cougars can become a contender for the division title and perhaps even for the pennant. They have prepared several proposals for free-agent acquisitions to present to the team's owner, Bruce Wayne. Under one proposal the team would sign several good available free agents, including two pitchers, a good fielding shortstop, and two power-hitting outfielders for $52 million in bonuses and annual salary. The second proposal is less ambitious, costing$20 million to sign a relief pitcher, a solid, good-hitting infielder, and one power-hitting outfielder. The final proposal would be to stand pat with the current team and continue to develop. General Manager Lane wants to lay out a possible season scenario for the owner so he can assess the longrun ramifications of each decision strategy. Because the only thing the owner understands is money, Frank wants this analysis to be quantitative, indicating the money to be made or lost from each strategy. To help develop this analysis, Frank has hired his kids, Penny and Nathan, both management science graduates from Tech. Penny and Nathan analyzed league data for the previous five seasons for attendance trends, logo sales (i.e., clothing, souvenirs, hats, etc.), player sales and trades, and revenues. In addition, they interviewed several other owners, general managers, and league officials. They also analyzed the free agents that the team was considering signing. Based on their analysis, Penny and Nathan feel that if the Cougars do not invest in any free agents, the team will have a 25% chance of contending for the division title and a 75% chance of being out of contention most of the season. If the team is a contender, there is a.70 probability that attendance will increase as the season progresses and the team will have high attendance levels (between 1.5 million and 2.0 million) with profits of $170 million from ticket sales, concessions, advertising sales, TV and radio sales, and logo sales. They estimate a.25 probability that the team's attendance will be mediocre (between 1.0 million and 1.5 million) with profits of$115 million and a.05 probability that the team will suffer low attendance (less than 1.0 million) with profit of $90 million. If the team is not a contender, Penny and Nathan estimate that there is.05 probability of high attendance with profits of$95 million, a.20 probability of medium attendance with profits of $55 million, and a.75 probability of low attendance with profits of$30 million. If the team marginally invests in free agents at a cost of $20 million, there is a 50-50 chance it will be a contender. If it is a contender, then later in the season it can either stand pat with its existing roster or buy or trade for players that could improve the team's chances of winning the division. If the team stands pat, there is a.75 probability that attendance will be high and profits will be$195 million. There is a.20 probability that attendance will be mediocre with profits of $160 million and a.05 probability of low attendance and profits of$120 million. Alternatively, if the team decides to buy or trade for players, it will cost $8 million, and the probability of high attendance with profits of$200 million will be.80. The probability of mediocre attendance with $170 million in profits will be.15, and there will be a.05 probability of low attendance, with profits of$125 million. If the team is not in contention, then it will either stand pat or sell some of its players, earning approximately $8 million in profit. If the team stands pat, there is a.12 probability of high attendance, with profits of$110 million; a.28 probability of mediocre attendance, with profits of $65 million; and a.60 probability of low attendance, with profits of$40 million. If the team sells players, the fans will likely lose interest at an even faster rate, and the probability of high attendance with profits of $100 million will drop to.08, the probability of mediocre attendance with profits of$60 million will be.22, and the probability of low attendance with profits of $35 million will be.70. The most ambitious free-agent strategy will increase the team's chances of being a contender to 65%. This strategy will also excite the fans most during the off-season and boost ticket sales and advertising and logo sales early in the year. If the team does contend for the division title, then later in the season it will have to decide whether to invest in more players. If the Cougars stand pat, the probability of high attendance with profits of$210 million will be.80, the probability of mediocre attendance with profits of $170 million will be.15, and the probability of low attendance with profits of$125 million will be.05. If the team buys players at a cost of $10 million, then the probability of having high attendance with profits of$220 million will increase to.83, the probability of mediocre attendance with profits of $175 million will be.12, and the probability of low attendance with profits of$130 million will be.05. If the team is not in contention, it will either sell some players' contracts later in the season for profits of around $12 million or stand pat. If it stays with its roster, the probability of high attendance with profits of$110 million will be.15, the probability of mediocre attendance with profits of $70 million will be.30, and the probability of low attendance with profits of$50 million will be.55. If the team sells players late in the season, there will be a.10 probability of high attendance with profits of $105 million, a.30 probability of mediocre attendance with profits of$65 million, and a.60 probability of low attendance with profits of $45 million. Assist Penny and Nathan in determining the best strategy to follow and its expected value. Essay Answer: Tags Choose question tag The owner of the Burger Doodle Restaurant is considering two ways to expand operations: open a drive-up window or serve breakfast. The increase in profits resulting from these proposed expansions depends on whether a competitor opens a franchise down the street. The possible profits from each expansion in operations, given both future competitive situations, are shown in the following payoff table: Select the best decision, using the following decision criteria. a. Maximax b. Maximin Essay Answer: Tags Choose question tag Mountain States Electric Service is an electrical utility company serving several states in the Rocky Mountains region. It is considering replacing some of its equipment at a generating substation and is attempting to decide whether it should replace an older, existing PCB transformer. (PCB is a toxic chemical known formally as polychlorinated biphenyl.) Even though the PCB generator meets all current regulations, if an incident occurred, such as a fire, and PCB contamination caused harm either to neighboring businesses or farms or to the environment, the company would be liable for damages. Recent court cases have shown that simply meeting utility regulations does not relieve a utility of liability if an incident causes harm to others. Also, courts have been awarding large damages to individuals and businesses harmed by hazardous incidents. If the utility replaces the PCB transformer, no PCB incidents will occur, and the only cost will be the cost of the transformer,$85,000. Alternatively, if the company decides to keep the existing PCB transformer, then management estimates that there is a 50-50 chance of there being a high likelihood of an incident or a low likelihood of an incident. For the case in which there is a high likelihood that an incident will occur, there is a.004 probability that a fire will occur sometime during the remaining life of the transformer and a.996 probability that no fire will occur. If a fire occurs, there is a.20 probability that it will be bad and the utility will incur a very high cost of approximately $90 million for the cleanup, whereas there is an.80 probability that the fire will be minor and cleanup can be accomplished at a low cost of approximately$8 million. If no fire occurs, no cleanup costs will occur. For the case in which there is a low likelihood that an incident will occur, there is a.001 probability that a fire will occur during the life of the existing transformer and a.999 probability that a fire will not occur. If a fire does occur, the same probabilities exist for the incidence of high and low cleanup costs, as well as the same cleanup costs, as indicated for the previous case. Similarly, if no fire occurs, there is no cleanup cost. Perform a decision tree analysis of this problem for Mountain States Electric Service and indicate the recommended solution. Is this the decision you believe the company should make Explain your reasons.