Posted: August 3rd, 2024

MAT540 Homework Week 2-A local real estate investor in Orlando is considering three alternative

MAT540 HomeworkWeek 2Page 1 of 4MAT540Week 2 HomeworkChapter 121.A local real estate investor in Orlando is considering three alternative investments; a motel, arestaurant, or a theater. Profits from the motel or restaurant will be affected by the availability ofgasoline and the number of tourists; profits from the theater will be relatively stable under anyconditions. The following payoff table shows the profit or loss that could result from eachinvestment:Weather ConditionsInvestmentShortageStable SupplySurplus$-7,500$12,000$23,000Restaurant30007,0006,500Theater50006,0004,000MotelDetermine the best investment, using the following decision criteria.a. Maximaxb. Maximinc. Minimax regretd. Hurwicz (α = 0.4)e. Equal likelihood2.A concessions manager at the Tech versus A&M football game must decide whether to have thevendors sell sun visors or umbrellas. There is a 35% chance of rain, a 25% chance of overcast skies,and a 40% chance of sunshine, according to the weather forecast in college junction, where thegame is to be held. The manager estimates that the following profits will result from each decision,given each set of weather conditions:MAT540 HomeworkWeek 2Page 2 of 4Weather ConditionsDecisionRainOvercastSunshine0.350.250.40Sun visors$-400$-200$1,500Umbrellas2,1000-800a. Compute the expected value for each decision and select the best one.b. Develop the opportunity loss table and compute the expected opportunity loss for eachdecision.3.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 anoffice building to rent, buying and leasing a warehouse, building a strip mall, and sellingcondominiums. The financial success of these projects depends on interest rate movement in thenext 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 in the following payoff table.Place-Plus real estate development firm has hired an economist to assign a probability to eachdirection interest rates may take over the next 5 years. The economist has determined that there is a0.45 probability that interest rates will decline, a 0.35 probability that rates will remain stable, and a0.2 probability that rates will increase.a. Using expected value, determine the best project.b. Determine the expected value of perfect information.Interest RateProjectDeclineStableIncreaseOffice park$0.4$1.55$3.5Office building2.51.82.75Warehouse1.71.451.5Mall0.82.33.5Condominiums3.21.50.5MAT540 HomeworkWeek 2Page 3 of 44.The director of career advising at Orange Community College wants to use decision analysis toprovide information to help students decide which 2-year degree program they should pursue. Thedirector has set up the following payoff table for six of the most popular and successful degreeprograms at OCC that shows the estimated 5-Year gross income ($) from each degree for fourfuture economic conditions:Economic ConditionsDegree ProgramRecessionAverageGoodRobustGraphic design150,000175,000220,000200,000Nursing160,000180,000205,000215,000Real estate125,000165,000220,000210,000Medical technology135,000180,000210,000270,000Culinary technology110,000145,000235,000205,000Computer information 130,000150,000190,000245,000technologyDetermine the best degree program in terms of projected income, using the following decision criteria:a. Maximaxb. Maximinc. Equal likelihoodd. Hurwicz (α=0.4)5.Construct a decision tree for the following decision situation and indicate the best decision.Fenton and Farrah Friendly, husband-and-wife car dealers, are soon going to open a new dealership.They have three offers: from a foreign compact car company, from a U.S. producer of full-sizedcars, and from a truck company. The success of each type of dealership will depend on how muchgasoline is going to be available during the next few years. The profit from each type of dealership,given the availability of gas, is shown in the following payoff table:MAT540 HomeworkWeek 2Page 4 of 4Gasoline AvailabilityDealershipShortageSurplus0.70.3Compact cars$25,000$150,000Full-sized cars-90,000650,000Trucks125,000170,000Decision Tree diagram to complete:Shortage 0.7$250,0002Surplus 0.31Full-sized cars$150,000Shortage 0.7Compact cars-$90,0003$650,000Surplus 0.3TrucksShortage 0.7$125,000Surplus 0.3$170,0004

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