MAT540 Week 8 Homework Latest 2017 March

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Question

MAT540

Week8 Homework

Chapter4

1. BettyMalloy,owneroftheEagleTaverninPittsburgh,ispreparingforSuperBowlSunday,and she mustdeterminehowmuchbeertostock.Betty stocksthreebrandsofbeer-Yodel,Shotz,and Rainwater.The costpergallon (tothetavern owner)ofeach brand isasfollows:

.gif”>Brand Cost/Gallon

.gif”>Yodel $1.50

Shotz 0.90

.gif”>Rainwater 0.50

The tavern has abudgetof$2,000forbeerforSuperBowlSunday.Betty sellsYodelatarateof

$3.00pergallon,Shotz at$2.50pergallon,and Rain waterat$1.75pergallon.Based on past football games, Bettyhasdeterminedthemaximumcustomerdemandtobe400gallonsofYodel,

500gallonsofshotz,and 300gallonsofRainwater. The tavernhas thecapacity to stock1,000 gallons ofbeer;Bettywants to stockup completely. Bettywants to determine thenumberofgallons ofeach brand of beerto ordersoasto maximize profit.

a. Formulatealinearprogramming model for thisproblem. b. Solve the modelbyusingthe computer.

2. Asresultofarecentlypassedbill,acongressman’sdistricthasbeenallocated$3millionfor programsandprojects.Itisup tothecongressmantodecide how to distributethemoney. The congressmanhasdecidetoallocate the money tofourongoing programsbecauseof their importancetohisdistrict-ajobtrainingprogram,aparksproject,asanitationproject,anda mobilelibrary.However,thecongressmanwantsto distributethemoney inamannerthatwill pleasethemostvoters,or, inotherwords,gainhim the mostvotesin theupcomingelection.His staff’sestimatesofthenumberofvotesgainedperdollarspent forthevarious programsareas follows.

Program

Votes/Dollar

Job training

0.03

Parks

0.08

Sanitation

0.05

Mobilelibrary

0.03

Inorderalsoto satisfyseverallocalinfluentialcitizenswhofinancedhiselection, heisobligated to observethefollowing guidelines:

· None ofthe programs can receivemore than 30%of the totalallocation

· Theamountallocatedtoparkscannotexceedthetotalallocatedtoboththesanitation projectandthe mobile library.

· Theamountallocatedtojobtrainingmustatleastequaltheamountspentonthesanitation project.

Anymoney notspentinthedistrictwillbereturnedtothegovernment;therefore,thecongressman wantstospenditall.Theecongressmanwantstoknowtheamounttoallocatetoeachprogram to maximize his votes.

a. Formulatea linearprogramming model for thisproblem. b. Solve the modelbyusingthe computer.

3. AnnaBroderick is the dietician for the StateUniversity football team,andshe isattempting to determineanutritiouslunchmenufortheteam.Shehassetthefollowingnutritionalguidelines for eachlunch serving:

· Between1,300 and 2,100 calories

· At least4mgof iron

· At least15 but no more than 55gof fat

· At least30gofprotein

· At least60gofcarbohydrates

· No more than 35mgofcholesterol

Sheselectsthemenufromsevenbasicfooditems,asfollows,withthenutritionalcontributions perpound and the cost as given:

Calories

(perlb.)

Iron

(mg/lb.)

Protein

(g/lb.)

Carbo-

hydrates

(g/lb.)

Fat

(g/lb.)

Cholesterol

(mg/lb)

Cost

($/lb.)

Chicken

500

4.2

17

0

30

180

0.85

Fish

480

3.1

85

0

5

90

3.35

Ground beef

840

0.25

82

0

75

350

2.45

Driedbeans

590

3.2

10

30

3

0

0.85

Lettuce

40

0.4

6

0

0

0

0.70

Potatoes

450

2.25

10

70

0

0

0.45

Milk(2%)

220

0.2

16

22

10

20

0.82

Thedieticianwantstoselectamenutomeetthenutritionalguidelineswhileminimizingthetotal cost perserving.

a. Formulatea linearprogramming model for thisproblemand solve.

4. Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determineaschedulefornursestomakesurethereareenoughofthemondutythroughoutthe day. Duringtheday,thedemandfornursesvaries. Maureenhasbrokenthedayintotwelve2- hourperiods.The slowesttimeoftheday encompassesthethreeperiods from 12:00A.M. to6:00

A.M.,whichbeginningatmidnight;requireaminimumof30,20,and40nurses,respectively. Thedemandfornursessteadilyincreasesduringthenextfourdaytimeperiods.Beginningwith the 6:00A.M.-8:00A.M. period,aminimumof50,60,80,and80nursesarerequiredforthese fourperiods,respectively.After2:00P.M. thedemandfornursesdecreasesduring theafternoon andeveninghours.Forthefive2-hourperiodsbeginningat2:00P.M.andendingmidnight,70,

70,60,50,and50nursesarerequired,respectively.Anursereportsforduty atthebeginning of oneof the2-hourperiods andworks8 consecutive hours (which is required in thenurses’ contract). Dr. Becker wants to determine a nursing schedule that will meet the hospital’s minimumrequirement throughout thedaywhile usingthe minimumnumberofnurses.

a. Formulatea linearprogramming model for thisproblem.

b. Solve the modelbyusingthe computer.

5. Theproduction managerofVideotechnics Companyis attemptingto determinethe upcoming5-month production schedule forvideo recorders. Past productionrecords indicate that 2,000 recorders can beproduced permonth. An additional 600 recorders can beproduced monthlyonan overtime basis. Unit cost is $10 for recorders produced

duringregularworkinghours and $15 forthose produced on an overtime basis. Contracted sales per month are as follows:

Month

Contracted Sales(units)

1

1200

2

2100

3

2400

4

3000

5

4000

Inventorycarryingcostsare$2 per recorder per month. Themanager does not want any inventorycarried over past the fifth month. Themanagerwants to know themonthly production that willminimizetotal production and inventorycosts.

a. Formulatealinear programmingmodel for this problem. b. Solve the model byusingthe computer.