MAT540 Week 2 Discussion
In your own words, explain how to obtain the “expected value of perfect information” for any payoff table, which has probabilities associated with each state of nature. Then, provide an example, drawing from any of the payoff tables in Problems 1-17 in the back of Chapter 12. If no probabilities are given for the states of nature, then assume equal likelihood.
MAT540 Week2 Homework
Chapter 12
1. AlocalrealestateinvestorinOrlandoisconsideringthreealternativeinvestments;amotel,arestaurant,oratheater.Profitsfromthemotelorrestaurantwillbeaffectedbytheavailabilityofgasolineandthenumberoftourists;profitsfromthetheaterwillberelativelystableunderanyconditions.Thefollowingpayofftableshowstheprofitorlossthatcouldresultfromeachinvestment:
Investment
|
|
Shortage |
Stable Supply |
Surplus |
|
Motel |
$-7,500 |
$12,000 |
$23,000 |
|
Restaurant |
3000 |
7,000 |
6,500 |
|
Theater |
5000 |
6,000 |
4,000 |
Determinethe bestinvestment, usingthe followingdecision criteria.
a. Maximax
b. Maximin
c. Minimax regret
d. Hurwicz(α =0.4)
e. Equallikelihood
2. AconcessionsmanagerattheTechversusA&Mfootballgamemustdecidewhethertohavethevendors sellsun visors orumbrellas.Thereis a 35% chance of rain, a 25% chance ofovercastskies,anda40%chanceofsunshine,accordingtotheweatherforecastincollegejunction,wherethegameistobeheld.Themanagerestimatesthatthefollowingprofitswillresultfromeachdecision,given each setofweather conditions:
Rain 0.35
Overcast0.25
Sunshine0.40
Sun visors $-400 $-200 $1,500
Umbrellas 2,100 0 -800
a. Compute the expected value foreach decisionand selectthe best one.
b. Develop the opportunitylosstableandcompute the expected opportunityloss foreachdecision.
3. Place-Plus,arealestatedevelopmentfirm,isconsideringseveralalternativedevelopmentprojects.Theseincludebuildingandleasinganofficepark,purchasingaparceloflandandbuildinganofficebuildingtorent,buyingandleasingawarehouse,buildingastripmall,andsellingcondominiums.Thefinancialsuccessoftheseprojectsdependsoninterestratemovementinthenext5years.Thevariousdevelopmentprojectsandtheir5-yearfinancialreturn(in$1,000,000s)giventhatinterestrateswilldecline,remainstable,orincrease,areinthefollowingpayofftable.Place-Plusrealestatedevelopmentfirmhashiredaneconomisttoassignaprobabilitytoeachdirectioninterestratesmaytakeoverthenext5years.Theeconomisthasdeterminedthatthereisa
0.45probability thatinterestrateswilldecline,a 0.35probability thatrates willremainstable, and a
1.2probabilitythatrates willincrease.
a. Usingexpected value, determine the bestproject.
b. Determinetheexpected value ofperfectinformation.
Project
|
|
Decline |
Stable |
Increase |
|
Office park |
$0.4 |
$1.55 |
$3.5 |
|
Office building |
2.5 |
1.8 |
2.75 |
|
Warehouse |
1.7 |
1.45 |
1.5 |
|
Mall |
0.8 |
2.3 |
3.5 |
|
Condominiums |
3.2 |
1.5 |
0.5 |
4. ThedirectorofcareeradvisingatOrangeCommunityCollegewantstousedecisionanalysistoprovideinformationtohelpstudentsdecidewhich2-yeardegreeprogramtheyshouldpursue.ThedirectorhassetupthefollowingpayofftableforsixofthemostpopularandsuccessfuldegreeprogramsatOCCthatshowstheestimated5-Yeargrossincome($)fromeachdegreeforfourfutureeconomic conditions:
DegreeProgram
|
|
Recession |
Average |
Good |
Robust |
|
Graphicdesign |
150,000 |
175,000 |
220,000 |
200,000 |
|
Nursing |
160,000 |
180,000 |
205,000 |
215,000 |
|
Realestate |
125,000 |
165,000 |
220,000 |
210,000 |
|
Medicaltechnology |
135,000 |
180,000 |
210,000 |
270,000 |
|
Culinary technology |
110,000 |
145,000 |
235,000 |
205,000 |
|
Computer information |
130,000 |
150,000 |
190,000 |
245,000 |
|
technology |
|
|
|
|
Determinethe bestdegreeprogramin terms ofprojected income, usingthefollowingdecisioncriteria:
a. Maximax
b. Maximin
c. Equallikelihood
d. Hurwicz(α=0.4)
5. Constructa decisiontreefor the followingdecision situation and indicate the bestdecision.
Fentonand Farrah Friendly,husband-and-wife cardealers, aresoon goingto open a new dealership.Theyhavethreeoffers:fromaforeigncompactcarcompany,fromaU.S.produceroffull-sizedcars,andfromatruckcompany.Thesuccessofeachtypeofdealershipwilldependonhowmuchgasolineisgoingtobeavailableduringthenextfewyears. Theprofitfromeachtypeofdealership,given the availabilityof gas, is shown inthe followingpayoff table:
Dealership
Shortage0.7
Surplus0.3
Compactcars $25,000 $150,000
Full-sized cars -90,000 650,000
Trucks 125,000 170,000
DecisionTreediagramto complete:
$250,000
$150,00
-$90,000
$650,000
$125,000
$170,000
