# Mat540 mat 540 mat/540 week 1 homework latest 2015

MAT540 Week 1 Discussion

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“Class Introductions”  Please respond to the following:

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.

a.       For anannualvolume of15, 000 tire, determine thetotalcost,total revenue, and profit.

b.      Determinetheannualbreak-even volume for the RetreadTire Companyoperation.

2.            EvergreenFertilizerCompanyproducesfertilizer.Thecompany’sfixedmonthlycostis\$25,000,anditsvariablecostperpoundoffertilizeris\$0.20.Evergreensellsthefertilizerfor\$0.45perpound. Determinethe monthlybreak-even volume for the company.

3.            IfEvergreenFertilizerCompanyinproblem2changesthepriceofitsfertilizerfrom\$0.45perpound to \$0.55perpound,whateffectwillthe change have on thebreak-even volume?

4.            IfEvergreenFertilizerCompanyincreasesitsadvertisingexpenditureby\$10,000peryear,whateffectwilltheincreasehave on the break-even volumecomputed inproblem2?

5.            AnnieMcCoy,astudentatTech,planstoopenahotdogstandinsideTech’sfootballstadiumduring homegames.There are6homegamesscheduledfor theupcoming season. Shemustpay theTechathleticdepartmentavendor’sfeeof\$3,000fortheseason.Herstandandotherequipmentwillcosther\$3,500 for the season.Sheestimates thateachhotdogshe sellswillcosther\$0.40. shehastalkedtofriendsatotheruniversitieswhosellhotdogsatgames.Basedontheirinformationandtheathleticdepartment’sforecastthateachgamewillsellout,sheanticipatesthatshewillsellapproximately1,500hot dogs duringeach game.

a.       Whatpriceshould she charge for a hotdoginordertobreakeven?

b.      Whatfactorsmightoccurduringtheseasonthatwouldalterthevolumesoldandthusthebreak-even price Annie mightcharge?

a.       How manystudents does the college need to enrollin the firstyearto break-even?

b.      If the college canenroll80students the firstyear,howmuch profitwillitmake?

c.       The collegebelievesitcan increasetuition to \$25,000, butdoing sowouldreduce enrollmentto

50. Should the college consider doingthis?Chapter 11

 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. Determine theexpected grade andvariance forthe course.

8.            Aninvestmentfirmisconsideringtwoalternativeinvestments,AandB,undertwopossiblefuturesetsofeconomicconditionsgoodandpoor.Thereisa.60probabilityofgoodeconomicconditionsoccurringanda.40probabilityofpooreconomicconditionsoccurring.Theexpectedgainsandlosses undereach 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,whatistheprobabilitythatthe renterswillnotbe ableto occupyin 18 months?

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

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