MAT540 Homework Week 2 Page 1 of 3 MAT540 Week 2 HomeworkChapter 12 1. A local real estate investor in Orlando isconsidering three alternative investments: a motel a restaurantor a theater. Profits from the motel or restaurant will be affectedby the availability of gasoline and the number of tourists; profitsfrom the theater will be relatively stable under any conditions.The following payoff table shows the profit or loss that couldresult from each investment: Gasoline Availability InvestmentShortage Stable Supply Surplus Motel $-8000 $15000 $20000Restaurant 2000 8000 6000 Theater 6000 6000 5000 Determinethe best investment using the following decision criteria. a.Maximax b. Maximin c. Minimax regret d. Hurwicz ( = 0.4) e. Equallikelihood 2. A concessions manager at the Tech versus A&Mfootball game must decide whether to have the vendors sell sunvisors or umbrellas. There is a 30% chance of rain a 15% chance ofovercast skies and a 55% chance of sunshine according to theweather forecast in College Junction where the game is to be held.The manager estimates that the following profits will result fromeach decision given each set of weather conditions: WeatherConditions Decision Rain Overcast Sunshine .30 .15 .55 Sun visors$-500 $-200 $1500 Umbrellas 2000 0 -900 a. Compute the expectedvalue for each decision and select the best one. b. Develop theopportunity loss table and compute the expected opportunity lossfor each decision. 3. Place-Plus a real estate development firmis considering several alternative development projects. Theseinclude building and leasing an office park purchasing a parcel ofland and building an office building to rent buying and leasing awarehouse building a strip mall and building and selling MAT540Homework Week 2 Page 2 of 3 condominiums. The financial success ofthese projects depends on interest rate movement in the next 5years. The various development projects and their 5-year financialreturn (in $1000000s) given that interest rates will declineremain stable or increase are shown in the following payofftable. Place-Plus real estate development firm has hired aneconomist to assign a probability to each direction interest ratesmay take over the next 5 years. The economist has determined thatthere is a .50 probability that interest rates will decline a .40probability that rates will remain stable and a .10 probabilitythat rates will increase. a. Using expected value determine thebest project. b. Determine the expected value of perfectinformation. Interest Rate Project Decline Stable Increase Officepark $0.5 $1.7 $4.5 Office building 1.5 1.9 2.5 Warehouse 1.7 1.41.0 Mall 0.7 2.4 3.6 Condominiums 3.2 1.5 0.6 4. The director ofcareer advising at Orange Community College wants to use decisionanalysis to provide information to help students decide which2-year degree program they should pursue. The director has set upthe following payoff table for six of the most popular andsuccessful degree programs at OCC that shows the estimated 5-yeargross income ($) from each degree for four future economicconditions: Degree Program Recession Average Good Robust Graphicdesign 145000 175000 220000 260000 Nursing 150000 180000205000 215000 Real estate 115000 165000 220000 320000 Medicaltechnology 130000 180000 210000 280000 Culinary technology115000 145000 235000 305000 Computer information technology125000 150000 190000 250000 Determine the best degree programin terms of projected income using the following decisioncriteria: a. Maximax b. Maximin c. Equal likelihood MAT540 HomeworkWeek 2 Page 3 of 3 d. Hurwicz ( = 0.50) 5. Construct a decisiontree for the following decision situation and indicate the bestdecision. Fenton and Farrah Friendly husband-and-wife car dealersare soon going to open a new dealership. They have three offers:from a foreign compact car company from a U.S. producer offull-sized cars and from a truck company. The success of each typeof dealership will depend on how much gasoline is going to beavailable during the next few years. The profit from each type ofdealership given the availability of gas is shown in thefollowing payoff table: Gasoline Availability Dealership ShortageSurplus .6 .4 Compact cars $ 300000 $150000 Full-sized cars-100000 600000 Trucks 120000 170000 Decision Tree
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