MAT 540 MAT/540 Week 3 Homework LATEST 2015

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MAT540 Week 3 Discussion

Discuss Simulation

Select one (1) of the following topics for your primary discussion posting:

Identify the part of setting up a simulation in Excel that you find to be the most challenging, and explain why. Identify resources that can help you with that.

Explain how simulation is used in the real world. Provide a specific example from your own line of work, or a line of work that you find particularly interesting.

 

MAT540 Week3 Homework

 

Chapter 14

 

1.            TheHoylakeRescueSquadreceivesanemergencycallevery1,2,3,4,5,or6hours,accordingtothefollowingprobabilitydistribution.Thesquad isonduty24 hours per day, 7 days per week:

 


TimeBetweenEmergency Calls(hr.)


Probability


1                                     0.15

2                                     0.10

3                                     0.20

4                                     0.25

5                                     0.20

6                                     0.10

 

1.00

 

 

 

a.       Simulatetheemergencycallsfor3days(notethatthiswillrequirea“running”,orcumulative,hourlyclock), usingtherandomnumbertable.

b.      Computetheaveragetimebetweencallsandcomparethisvaluewiththeexpectedvalueofthetime between calls fromtheprobabilitydistribution.Whyare the resultdifferent?

2.            ThetimebetweenarrivalsofcarsatthePetrocoServicesStationisdefinedbythefollowingprobabilitydistribution:

 


TimeBetweenEmergency Calls(hr.)


Probability


1                                     0.35

2                                     0.25

3                                     0.20

4                                     0.20

 

1.00

 


 

a.       Simulatethearrivalofcarsattheservicestationfor20arrivalsandcomputetheaveragetimebetween arrivals.

b.      Simulatethearrivalofcarsattheservicestationfor1hour,usingadifferentstreamofrandomnumbers fromthose used in(a)and compute the average time betweenarrivals.

c.       Compare theresults obtained in(a) and(b).

3.      TheDynacoManufacturingCompanyproducesaproductinaprocessconsistingofoperationsoffivemachines.Theprobabilitydistributionofthenumberofmachinesthatwillbreakdowninaweekfollows:

 


MachineBreakdownsPer Week


Probability


0                                     0.10

1                                     0.20

2                                     0.15

3                                     0.30

4                                     0.15

5                                     0.10

 

1.00

 

 

 

a.       Simulatethe machine breakdowns per weekfor20 weeks.

b.      Compute the average numberofmachinesthatwillbreakdown perweek.

 

 

4.            Simulatethefollowingdecisionsituation for 20 weeks, andrecommend the bestdecision.

 

AconcessionsmanagerattheTechversusA&Mfootballgamemustdecidewhethertohavethevendors sellsun visors orumbrellas.Thereis a 30% chance of rain, a 15%chance ofovercastskies,anda55%chanceofsunshine,accordingtotheweatherforecastincollegejunction,wherethegameistobeheld.Themanagerestimatesthatthefollowingprofitswillresultfromeachdecision,given each setofweather conditions:


 

Decision                                                     Weather Conditions

 

 

Rain

Overcast

Sunshine

0.35

0.25

0.40

Sun visors

$-400

$-200

$1,500

Umbrellas

2,100

0

-800

 

 

5.            Everytime amachine breaks down at the Dynaco ManufacturingCompany(Problem3), either1, 2,or 3 hoursarerequiredto fix it,accordingto the followingprobabilitydistribution:

 

Repair Time (hr.)

Probability

1

0.20

2

0.50

3

0.30

 

1.00

 

 

 

Simulatetherepair time for20 weeks andthencompute theaverage weeklyrepairtime.

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