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Qumlon: solve rne lollowlng synem o1- llnear equaoons uxlrlg me sllbunlnn memoo: M_w=m 5:: + 10y = _ 10 Express Illswer as an ammo palr. Wmmmmmnwmummmnmnmmmk Mmplsofmnarymmrspam: (2.3) (-5.4) {6:11) e Quorum 2 solve rne lollowlng sysoem of llnear eouarlons uslng are sumnurlon memo: 1 a _ I\" + 79 11 ~ %x + %y = 3 (J Expmi answer a; an omeqeo palr. Enreronswer wrrn no war oerwem alpnanurnerie momma. pom and symbols. Emmpl: almmtrcmued moms.- (1'3) (-1") (5"11) Won 5 solve rlre lollowlnp synem ol- llnear equauons usurp me aoolrlon memoo: 21 + 551 = 42 7: + 21; = 30 Expreu anoweru an ordered pair. :nlor onrwnr wirn no spa-25 men ulpnanumm'c charm paranlnsos. onosyrnuolr. Brornpla: morn-cum Its-poms: (Z3) (-54) (5,11) Question 4 solve me lollmnng symlll rt llnear equarlons uslng me lddlllon method: Gz 5y = 34 2x + 61; = 4 Exprese .Imweruln melee pair. Enmmwhnnaspammmulpmmmicmmmmmmww. Brumpuxbfmmcy-mnsponsu: (2,3) (-5,-4) (o-n) Quartiml 5 A puirar lacoory has nd prooualon cm of \"mm plus :75 flu each guirar proouoro. n: can of plwumml rvnmon an o- me'ln isqx) =75X' 50,000. Tm mmpany oeclaasoo Mum punarlor ms, so lrs mlllue luncuon oan oawrlrnn as nor) =zzsx. How many Quint! mm are mmplrly sell an 3315 net ulnar in older no 'break even'? Woman 6 when nlrea as a new [oh selllng elemrnlcs, you are glven rwo ply oprlons: o mm A: Baa: salary 314.000 a yaarwlm a oommiscion of 10% ofywsahs o oprlon a: Babe salary ovszonloo a yearwlm a oomrnlsslon oulloryoursalac. Aner what amount of your sales (or s) does option A proouce a lalgel paycheck far you? :mernnsweros o numoerwnnouuxlnn orwmmas. Examplesbfmnrmy-Imuldlupomm 45m 21500 103900 Quinlan 1 A nlovlng company ale-per a llar me of 3150, am: an aoalrlonal ss tor earn box. A oellvery same would alarge nu tor eam box. Aloer now nuny ooxeswoulo lloe cheaperm use me Illang oompeny? In rm graph abovl. Mum m or corn-r palms udms ma feasihu roglon for ma (alumna rymm or umar lllaquanns: z+3y218 21+y516 $20 yZO O (o, s) :(o. 16) ; (a. 4) (neginn ll) 0 (6,4) :(8. l7) :(13, a) (neglon IV) O M15):(6-4):(r) (Regianl) d. P = 320cc 240g 9 (vi) Which orthe following sets orcomar points windy denestha feasible region ior this symnt of linear inequalities? (Enter lctterfor correct answer in the crank; a. (0, 320); (so, 160); (240, 0) b. (0, 240); (80, 160); (160, 0); (0, 0) c. (0, 240); (0, 320); (80, 160) d. (160, 0); (240, 0); (so, 160) 2; MI) laud an your determination atthe ieaclhle reglan tor this hutineas prose-e. haw many acres otoorn and of one should be planted to maximise prot? (Enter letter for correct answer in the blank) a. 160 acres of corn and 0 acres of oats b. 240 acres of corn and 0 acres of cats c. 30 acres of corn and 160 acres ofoats or None of these answers are correct '5 (viii) which otthe folliwwing is the correct value iornae amount ottatal maximum prot fnml raising the optimum acrea oiute two crops? a. $8000 b. $9600 c. $7200 d. $6400 Question 15 salvo using the graphical method. choose your variables, idantiry the oltiectm Motion and the constraints. graph the constraints, shade the icasllriuty region. identity au corner points, and determine the solution that opllmlus the objective iunctiorr, Use this lntormatior. to answer the rouowing s-oart queninn: A city council voted (0 oonduct a study on inner-city community piobLems using snciulugisls and research assistants irom uMuc, Allocation of time and costs per week are given in the iollowrrig table: labor hours MINIMUM laoor Laoor hours - , research hours needed per Sociologisc . assistant week Fieldwork 10 so 130 Research 30 10 140 center Cnsls per $500 5300 week (I) Which varlahle should it dene? (Enter letter far aorrecr answer in the blank} a. Imal amounl of labor hours needed for sociologisis o. numoer or sociologists needed tor the study c. total numoer oi Label-hours needed for research assistants d. totalnurniaer of study team members needed '5 (ll) Which va ole should ydenet (Enter leiterfar correct answer in the blank) a. Imal number or snidy team memoers needed a. coral numoer oi iaoor-hours needed far research assislanrs c. total numoer oi Labor-hours needed for sociologists d. number of research assistanls needed for the study '5 (iii) Which ortherollowlitg correctly denes the constraint on numoerorlaltor hours for eldwerk? (Enter lenerfar correct answer in the blank) a. 30m + 10y 2 140 b. 30:: + 10y S 140 c. 10.2 + 301/ Z 180 d. 10:: + 303/ g 180 -.-; (iv) Which otuie tollauring correctly denes the constraint an labor-hours needed at the reeearch oentert (Enter letter/or correct answer in the blank) (1 303: + 103/ Z 140 b 303: + 10y S 140 c. 103: + 30g 2 180 d 10m + 30y 3 180 (V) Which otthe iollawing my denes the olrlective itrncticrtz (Enter letter for correct answer in the blank) a C = 10a + 3011 b. C = 302 + 109 c C : 5002 + 300y d. c = 3002 + 5009 "J (vi) Which otthe ioliowlng sets oreorner points correctly dear-es theieasioie region ior this system otlinear ineouatlties? (Enter letter [or correct answer in the blank) 11. (0, 14) ; (0, 6) ; (3, 5) b. (0, 14) ; (3, 5) ; (18, 0) c. (0, 6) ; (3, 5) ; (18, 0) d- (0, 6) ; (3r 5) (5i 0) ; (0i 0) '9 (vii) Based on your determination oftha feasihla region for this business process, how many sociologists and how many research assistants shouLd be hired to complete this study for minimum cost? (Enter letter for correct answer in the blank; 3. 3 sociologists and 5 research assistants h. 0 sociologists and 14 research assistants c, IE sociologists and 0 research assistants t1. None of these answers are correct e; (VIII) which of"! fulhwdlng ll sh: tuned VII\"! for III: llilnlnlum (an (a mmplm ml! sludy? a. C = $2500 11. C $3000 0. C' : $4200 d. C' = $9000 \fQuestion 11 In the graph zbuve. the HNEOHNDED teasible region is dened by which system of linear inequalities? z+3y218 02o+yg16 $20 yZO z+3y18 O2w+y216 1:20 (/20 z+31118 02o+yg16 2:20 )120 )uestion 12 solve thing the grephlcal method. choeee your variabliet identity the oblective hrncdon Ind the cenatralnte graph the otnnrelnte. tirade tha ieeslbility region. ldantliy all oorner points. and determine the eoitrtlon met optlmlntt the objective illnetlon. llee chit intonrtetlon to am the (may open question: A small company manulactures two types of radios- regular and shornwavetne manufacturing of each radio requirestwo operations: Assembly and Finishing. The regular radios require 1 hour orAssembiy and 3 hours of Finishlng. The shortwave radios require 3 hours ofAssemly and 1 hour o1 Finishing, the total laboHiours available per week in the Assembly division is so. and in the Finishing division. so. A protltot :50 is realized (or every regular radio and 375 (or every shortwave radio. Management wants to deterrnine the number or each type or radio to produce so that prol'rt can be maximized. (I) wtilrh variable should it dllnl? (Enter letter/or coma answer in trre blank) a. number of regular radios produced or number or labor-hours needed tor assembly c. total number or radios to produce in orderro maximize piorrt do number or laboHtoliis needed iorhnishlng '9 (it) Which we able should ydlnl? (Enter letter [or correct answer in the blank) a. wtal number of radiosbo produce ln orderto maximize prot b, number otshort-wave radios produced c, number oi labor-hours needed for assembly d, numberot laborhours needed for hnlshinn 1') (iii) wnlch ottne MW\" correctty delines the constraint on labor-noun ior radio eeremblyt (Enter letter In! correct answer in the blank] o. 3n + y g 60 b. a + 3y 5 60 c. z + 3y 2 60 d 3:: + y 2 60 '9 (hr) whim ettna humming oerredty dennes m mnmlm on labonnauis needed no radio rlnlsnlngz (Enter letter jar eonert answer in the blunt; o. 3:: + y 2 60 b. a + 3y 2 60 or z + 3y g 60 d. 3:1: + y s so '5 M whim orthe iollowlng oorrecuy dehrles the obienive lirrlotionz (Enter letter/or oorrest answer in "it blank) o. P : 60:: + 609 b P = 752 + 50y c. P = 502 + 75y d. P : 300:: + 45001; '3) (vi) wnlrn ottiie toliorrlng setsotiesmerpoints coneetly detir-stteieaslble ieglontortnis syn-m otlinear iwnlltiu? (Erner letter for oerrect answer in the blank; o. (0,20) ; (0, 60); (15,15) 17. (0, 20) ; (0, 0) ; (20,0); (15.15) c. (0, 60); (15,15); (60, 0) d. (15,15) ; (20, 0) ; (60,0) '3) (vii) laced on your determination otthe ieatlble region tor thit btialrieeo process how many radios of each type trtould be produoed ln orderto merilmiae prom (Enter letter jbr mm answer in the blank) a. 0 regular radios and to shortwave radios b. 20 regular radios and o shortwave radios c 15 regular radios and 15 shortwave radios d. 0 regular radios and on shortwave radios '3 (viii) wnlrn otttre totlorrrlng is the correct value torthe maalmum total prot made tnirn producing the optimum rnrmber at each type ot ladlu? a. P : $4500 12. P : $3000 at P $1500 ii P = $1875 '9 Question 15 Solve using the graphical method, choose your variables. identity the old-ave nrnctilon and the mints. graph the constraints. shade the teaslblllty region identity all comer points. and determine the soliitlon that optimizes the obleettee ninetlon. use this lnromiatlon to amr tare rotlorclng a-part daemon: A company produces twotypes or shoes - usual. and athletic ~ at its two tactories. Facaoryl and Factory ||. Daily production at each iacoory for number of it of each type otshoe is listed below: Factory | Factory || casual we no Athletic zoo loo the oompany must produce at least two pairs otcasuai shoes. and 9on0 pairs of emetic shoes. The cost or operating Factory | is moo per day and the cost of operating Factory II is moo. Management needs to deterrnine the number otdays each iactory needs to operarero meet production goals at minimum cost (l) Which variable should it detin-z isnoer letter jar correa answer in the blank; a. number of pairs or athletic shoes produced it number or days Factory | operates c number or pairs oicasdal shoes produced a. some proouoe a pair oratnietic snoes '3 (it) Which variable should ydetinet (Enter letter [or correct answer in the blank) a. number of pairs of athletic shoes produced b eostro produoe a pairotoasuat shoes c number or pairs or casual shoes produced d. number or days Famry it operates '9 (ill) wnirrl ot the billowing correctly Mines the Walm on total daily produaion M pairs of usual mm? (Enter letter jbr oonett answer in the blank} a. 2001 + 100); 5 8000 b. 100:: + 2003; 5 8000 c. 200:: + 1003} Z 8000 d. 100m + 2001/ 2 8000 5 (IV) Which or the blowing correctly delinee the ooiisttelnt on total daily production of pairs of athletic \"In\"? (Enter letter [or oorreet answer in the blank] :1. 300:: + 1003; 2 9000 b 1001 + 3003; 2 9000 c. 300:: + 1003; 5 9000 d 100:: + 300;; 5 9000 7 (v) wnlctr ottha follMitg correctly dlnl: the obj-dive iunetioni (Enoer letter [or correct answer in the blank) (I. C : 8000:: + 9000); b. C = 90002 + 800011 c. C = 1500:: + 20003; d C = 2000.7: + 1500); '3 (v1) wnlcb otthe renewing ms ot comer points oorremy dehriet the ieatlble region iarthlt tyeotnr of linear lnoqiumils'.' (Enter letter for other: answer in the bianld a- (D) 0); (40, 0); (20i 30); (30i 0) b (0, 4o); (0, 90); (20, 30) c. (o, 90); (20, 30); (so, 0) a. (20, 30); (30, 0); (so, 0) 9 (vii) land on your mmllmian orth- ieatlble region (or tnlt business WWI: m many dayt should tam restory mm to meat production goals at minimum and: (Enter letter jar correct answer in the blank) a. so days tor Factory I and a days (or Factory il b. 20 days tor Factoryl and so days for Factory II c 0 days (or Factory | and 40 days tor Factory II o. None otthesa answers are oorract 9 (viii) wnlcn ot the (allowing is the oonect value tor the minimum cost to meet pioducblon goals tor both qpes otstroes't a. C : $45000 b. C = $80000 c. C = $90000 do 0 = $ 120000 9 save Question 14 solve using the graphical method. choose your variables, ldentliythe objective ninctlon and the oonmlnn. own the oonstrai ,citade the ieasiblllty region, identity ali mm polnts. and deterrnlne the solution that optimises the obj-Give nincdort lise tnis intonnatlon to answertlre (allowing t-part qumlun: sunnydaie Farms has a total 07140 acres at cropland. The larm owner wantsbo plant this acreage in corn and oats. Ari acre oi corn brings m in proilt. and an acre otoats gets no pram. A total o1 no IzboHiours to raise the crops is available. Each acre otoom needs 1 labo hours and each acre ototts needs a labor~haur. The term owner wantsto optimize the planting oi the m aeresoo mate m um protir. (l) Which variable snould tr Mm? (Enter letterydr when answer in the blow a. total amount otpront made irom planting corn b. numberot labor-hours ior optimum oats planting c. number of labor-hours (or optimum corn planting d. number otacres or corn planted '9 (ll) wnich variable should y Mlle? (Enter letterfer correct answer in the plant) a, number of acres M oats planted b. number of labor-hours fur optimum oats planting r, number of labor-hours ior optimum corn planting d. total amount or protir made irom planting oats '9 (ill) wnlch ottire taliiowlng mectty detlnes the constraint on ootal acres ot cropland available (or piairtlng? (Enter letter for correct answer in the blank) a. 40o+3opg 24o 2I+IIS320 sari/$240 401+30y320 9-9? '5 (M whim of"!- bwn non-my 1.0!!\" "II Gum-Int an labor-noun will\"! '01 hmllnil' (Enter (MM Dom answer in the blank] o. :1: + y g 240 b. a + y g 320 c. 21: + y g 240 d. 2:: + y s 320 '5' (v) whlm otttre rotiowlng coneetty delines the oblectlw nuicdonz (Enter letter [or oorieet answer in the plant; a. P=z+y b. P=40z+30y c. P:Zz+u