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Please introduce yourself, including your educational and career goals, as well as some personal information about yourself. In your introduction, please draw from your own experience (or use a search engine) to give an example of how probability is used in your chosen profession. If you get your information from an online or other resource, be sure to cite the source of the information

MAT540 Week1 Homework

 

Chapter 1

 

1. TheRetreadTire Companyrecapstires.Thefixedannual  cost  of  the  recappingoperation  is

$65,000.The variable costof recappinga tire is $7.5.Thecompanycharges$25to recap atire.

1. For anannualvolume of15, 000 tire, determine thetotalcost,total revenue, and profit.
2. Determinetheannualbreak-even volume for the RetreadTire Companyoperation.
3. EvergreenFertilizerCompanyproducesfertilizer.Thecompany’sfixedmonthlycostis$25,000,anditsvariablecostperpoundoffertilizeris$0.20.Evergreensellsthefertilizerfor$0.45perpound.Determinethe monthlybreak-even volume for the company.
4. IfEvergreenFertilizerCompanyinproblem2changesthepriceofitsfertilizerfrom$0.45perpound to$0.55perpound,whateffectwillthe change have on thebreak-even volume?
5. IfEvergreenFertilizerCompanyincreasesitsadvertisingexpenditureby$10,000peryear,whateffectwilltheincreasehaveon the break-even volumecomputed inproblem2?
6. AnnieMcCoy,astudentatTech,planstoopenahotdogstandinsideTech’sfootballstadiumduringhomegames.There are6homegamesscheduledfor theupcoming season. Shemustpay theTechathleticdepartmentavendor’sfeeof$3,000fortheseason.Herstandandotherequipmentwillcosther$3,500for the season.Sheestimates thateachhotdogshe sellswillcosther$0.40.shehastalkedtofriendsatotheruniversitieswhosellhotdogsatgames.Basedontheirinformationandtheathleticdepartment’sforecastthateachgamewillsellout,sheanticipatesthatshewillsellapproximately1,500hotdogs duringeach game.
7. Whatpriceshould she charge for a hotdoginordertobreakeven?
8. Whatfactorsmightoccurduringtheseasonthatwouldalterthevolumesoldandthusthebreak-even priceAnnie mightcharge?
9. ThecollegeofbusinessatKerouacUniversityisplanningtobeginanonlineMBAprogram.Theinitialstart-upcostforcomputingequipment,facilities,coursedevelopmentandstaffrecruitmentanddevelopmentis$400,000.Thecollegeplanstochargetuitionof$20,000perstudentperyear.However,theuniversityadministrationwillchargethecollege$10,000perstudentforthefirst100studentsenrolledeach yearfor administrative costsanditsshare of thetuition payments.
10. How manystudents does the college need to enrollin the firstyearto break-even?
11. If the college canenroll80students the firstyear,howmuch profitwillitmake?

 

 

1. The collegebelievesitcan increasetuition to $25,000, butdoing sowouldreduce enrollmentto
2. Should the college consider doingthis?Chapter 11
3. Thefollowingprobabilitiesforgradesinmanagementsciencehavebeendeterminedbasedonpastrecords:

 

Grade	Probability
A	0.1
B	0.2
C	0.4
D	0.2
F	0.10
	1.00

 

 

Thegradesareassigned ona 4.0 scale, where anAisa4.0, a B a 3.0, andso on. Determinetheexpected grade andvariance forthe course.

 

8. Aninvestmentfirmisconsideringtwoalternativeinvestments,AandB,undertwopossiblefuturesetsofeconomicconditionsgoodandpoor.Thereisa.60probabilityofgoodeconomicconditionsoccurringanda.40probabilityofpooreconomicconditionsoccurring.Theexpectedgainsandlossesundereach economic type ofconditions areshown in the followingtable:

 

Economic Conditions

Investment                                                                                     

	Good	Poor
A	$380,000	-$100,000
B	$130,000	$85,000

 

 

Usingthe expected value ofeachinvestmentalternative, determine which shouldbe selected.

 

9. Theweightofthebagsoffertilizerisnormallydistributed,withameanof45poundsandastandarddeviationof5pounds.Whatistheprobabilitythatabagoffertilizerwillweighbetween38 and 50pounds?

 

 

10. ThepoloDevelopmentFirmisbuildingashoppingcenter.Ithasinformedrentersthattheirrentalspaceswillbereadyforoccupancyin18months.Iftheexpectedtimeuntiltheshoppingcenteriscompletedisestimatedtobe15months,withastandarddeviationof5months,whatistheprobabilitythattherenterswillnotbe ableto occupyin 18 months?

 

11. ThemanagerofthelocalNationalVideoStoresellsvideocassetterecordersatdiscountprices.Ifthestoredoesnothaveavideorecorderinstockwhenacustomerwantstobuyone,itwilllosethesalebecausethecustomerwillpurchasearecorderfromoneofthemanylocalcompetitors.Theproblemisthatthecostofrentingwarehousespacetokeepenoughrecordersininventorytomeetalldemandisexcessivelyhigh.Themanagerhasdeterminedthatif85%ofcustomerdemandforrecorderscanbemet,thenthecombinedcostoflostsalesandinventorywillbeminimized.Themanagerhasestimatedthatmonthlydemandforrecordersisnormallydistributed,withameanof175recordersandastandarddeviationof55.Determinethenumberofrecordersthemanagershouldordereach monthtomeet85% of customerdemand.