MAT540 Week 2 Homework

| August 30, 2017

uestion
MAT540 Week2 Homework

Chapter 12

1. Alocal real estate investor in Orlando is considering three alternative investments;amotel,arestaurant,oratheater.Profitsfromthemotelorrestaurantwillbeaffectedbytheavailabilityofgasolineandthenumberoftourists;profitsfromthetheaterwillberelativelystableunderanyconditions.Thefollowingpayofftableshowstheprofitorlossthatcouldresultfromeachinvestment:

Weather Conditions

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(? =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

Sunshine0.40

Sun visors $-400 $-200 $1,500

Umbrellas 2,100 0 -80

a. Compute the expected value foreach decisionand selectthe bestone.

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

1.2 probabilitythatrates willincrease.

a. Usingexpected value, determine the bestproject.

b. Determinetheexpected value ofperfectinformation.

Interest Rate

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:

Economic Conditions

DegreeProgram

Recession

Average

Good

Robust

Graphic design

150,000

175,000

220,000

200,000

Nursing

160,000

180,000

205,000

215,000

Real estate

125,000

165,000

220,000

210,000

Medical technology

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(?=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:

Gasoline Availability

Dealership

Shortage0.7

Surplus0.3

Compactcars $25,000 $150,000

Full-sized cars -90,000 650,000

Trucks 125,000 170,000

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