MATH 534 Week 2 Addendum: Homework-Quiz Review
i i i i i i
.
1 Gina iFox ihas istarted iher iown icompany, iFoxy iShirts, iwhich imanufactures iimprinted ishirts
iforispecial ioccasions. iSince ishe ihas ijust ibegun ithis ioperation, ishe irents ithe iequipment ifrom
ia ilocal iprinting ishop iwhen inecessary. iThe icost iof iusing ithe iequipment iis i$350. iThe
imaterials iused iin ione ishirt icost i$8, iand iGina ican isell ithese ifor i$15 ieach.
(a) How imany ishirts imust iGina isell ito ibreak ieven?
(b) What iis ithe itotal irevenue ifor ithis?
Mark iyour ianswer icarefully. iPartial icredit iwill ibe iawarded ieither ipart-a ior ipart-bianswer
icorrectly iand ifull icredit iif iboth iparts iare ianswered icorrectly
Selectedi
Answer:
Part-a) i50 iand iPart-b) i750
f i = i 350 s i = i 15 v i = i8
Responsei f i = i 350 s i = i 15 v i = i8
Feedback: a) iBEP i = if/(s i − iv) i = i350/(15 i − i8) i = i50 iunits
b)Total irevenue = 50(15) = $750
If iGina isells i20 ishirts, iwhat iwill iher itotal irevenue ibe? iWhatiwill
iher itotal ivariable icost ibe?
c) iTotal irevenue i = i20(15) i = i$300
id))Total ivariable icost i = i20(8) i = i$160
2 i.
A icouple iof ientrepreneurial ibusiness istudents iat iFrostburg iState iUniversity idecided ito iput
itheir ieducation iinto ipractice iby ideveloping ia itutoring icompany ifor ibusiness istudents.
iWhileiprivate itutoring iwas ioffered, iit iwas idetermined ithat igroup itutoring ibefore itests iin ithe
ilarge istatistics iclasses iwould ibe imost ibeneficial. iThe istudents irented ia iroom iclose ito icampus
ifor
$300 ifor i3 ihours. iThey ideveloped ihandouts ibased ion ipast itests, iand ithese ihandouts
i(including icolor igraphs) icost i$5 ieach. iThe itutor iwas ipaid i$25 iper ihour, ifor ia itotal iof i$75
iforieach itutoring isession.
(a) If istudents iare icharged i$20 ito iattend ithe isession; ihow imany istudents imust ienroll ifor
itheicompany ito ibreak ieven?
(b) A isomewhat ismaller iroom iis iavailable ifor i$200 ifor i3 ihours. iThe icompany iis
iconsideringithis ipossibility. iHow iwould ithis iaffect ithe ibreak-even ipoint?
Mark iyour ianswer icarefully. iPartial icredit iwill ibe iawarded ieither ipart-a ior ipart-bianswer
icorrectly iand ifull icredit iif iboth iparts iare ianswered icorrectly
Part-a) iBEP i= i25 i Part-b) iBEP i= i18.33
Responsei a) i f i = i 300 i + i 75 i =
Feedback: i375 s i = i 20 iv i = i 5
BEP i = if/(s i– iv) i = i375/(20 i–
, BEP i = if/(s i − iv) i = i275/(20 i − i5) i =
i 1i8.333
3. What iis ithe iformula ifor ithe ibreak-even ipoint iof ia isimple iprofit imodel?
Fixed iCost i/ i(Selling iPrice iPer iUnit i- iVariable iCost iPer iUnit)
4.
Trying ivarious iapproaches iand ipicking ithe ione ithat iresults iin ithe ibest idecision iis icalled
the itrial-and-error imethod.
Question i5
Evaluating iall ipossible ivalues iof ia ivariable iin ia imodel iis icalled
Selected iAnswer: i complete ienumeration.
Question i6
Which iof ithe ifollowing iterms iis iinterchangeable iwith iquantitative ianalysis?
Selected iAnswer: management iscience
Question i7
The iwidespread iapplicability iof ioperations iresearch imethods ito ibusiness ifollowed
iwhichiwar?
Selected iAnswer: i World iWar iII
Question i8
Which iof ithe ifollowing itechniques iinvolves ithe iuse iof ioptimization imethods ito iprovide inewiand
ibetter iways ito ioperate ibased ion ispecific ibusiness iobjectives?
Selected iAnswer: i prescriptive ianalytics
Expressing iprofits ithrough ithe irelationship iamong iunit iprice, ifixed icosts, iand ivariable icosts iisian
iexample iof
Selected iAnswer: i a iquantitative ianalysis imodel.
Question i10
Which iof ithe ifollowing iis inot ione iof ithe isteps iin ithe iquantitative ianalysis iapproach?
Question i11
Which iof ithe ifollowing iis ia ipicture, idrawing, ior ichart iof ireality?
Question i12
,All iof ithe ifollowing iare ireal icomputer iapplications ithat iperform iquantitative ianalysis iexcept
QA i for i Windows
Question i13
Decision ivariables imay ialso ibe icalled iparameters.
Selected iAnswer: iFalse
Question i14
A icontrollable ivariable iis ialso icalled ia variable.
decision
Question i15
Models ican ihelp ius ianalyze ia iproblem iand isell ia idecision ito ithose iwho imust iimplement iit.
True
Question i16
Management isupport iand iuser iinvolvement iare inot iessential iin ithe
isuccessfuliimplementation iof iquantitative ianalysis iprojects.
Selected iAnswer: i False
Question i17
Interviews, istatistical isampling, iand icompany ireports iprovide iinput idata ifor
iquantitativeianalysis imodels.
True
Question i18
A imathematical imodel ishows ithe irelationship ibetween iquantifiable iand inon-
quantifiableiinformation.
Selected iAnswer: i False
Question i19
When ia iproblem iis idifficult ito iquantify, iit imay ibe inecessary ito idevelop iunspecific iobjectives.
Selected iAnswer: i False
Question i20
Business iAnalytics iis ia idata-driven iapproach ito idecision imaking ithat iallows icompanies
itoimake ibetter idecisions.
M i3
QU iE STION i 1
Which iof ithe ifollowing iis ia irequired icondition ifor ia idiscrete iprobability ifunction?
, D. i∑p(x) i= i1 ifor iall ivalues iof ix
5 ipoints
QU iE STION i 2
Assume iyou ihave iapplied ifor itwo ischolarships, ia iMerit ischolarship i(M) iand ian
iAthleticischolarship i(A). iThe iprobability ithat iyou ireceive ian iAthletic ischolarship iis i0.18. iThe
iprobability iof ireceiving iboth ischolarships iis i0.11. iThe iprobability iof igetting iat ileast ione iof
ithe ischolarships iis i0.3.
a). Are ievents iA iand iM imutually iexclusive? iWhy ior iwhy inot?
Two ievents iare isaid ito ibe imutually iexclusive iif ithe ievents ihave ino isample ipoints iin
icommon.iThat iis, itwo ievents iare imutually iexclusive iif, iwhen ione ievent ioccurs, ithe iother
icannot ioccuri(i.e. iP(MA) i= i0)
P(A iM) i =.3 i ≠ i 1 i and i P(A i ∩ i M) i =.11 i ≠ i 0 i A i and i M i are i not i mutually i exclusive.
b). Are ithe itwo ievents iA, iand iM, iindependent? iWhy ior iwhy
not?iTwo ievents iA iand iB iare isaid ito ibe iindependent iif iand
i
only iif:
i
P(A i∩ iM)P(A|B)
i=.11 i= iP(A) ior,P(A)
iequivalently,
iP i(M) i=.18 ix.P(B|A) i= iP(B)
i23 i= i.0414 i≠ iP(A i ∩ iM)
Therefore, iA iand iM iare inot iindependent.
.
Mark iyour ianswer icarefully. iPartial icredit iwill ibe iawarded ieither ipart-a ior ipart-
bianswer icorrectly iand ifull icredit iif iboth iparts iare ianswered icorrectly
Part ia) i No, ibecause iP(A i∩ iM) i≠ i0
Part ib) i No, ibecause iP(A i∩ iM) i≠ iP(A) iP(M)
QU iE STION i 3
Assume iyou ihave iapplied ifor itwo ischolarships, ia iMerit ischolarship i(M) iand ian iAthletic ischolarship
i(A).iThe iprobability ithat iyou ireceive ian iAthletic ischolarship iis i0.18. iThe iprobability iof ireceiving iboth
ischolarships iis i0.11. iThe iprobability iof igetting i at ileast ione iof ithe ischolarships iis i0.3.
a. What iis ithe iprobability ithat iyou iwill ireceive ia iMerit ischolarship? i**"at ileast" iis ianother
iwordifor ithe iunion iof itwo ievents. iThe iunion iformula ishould ihelp iyou iwith ithis iproblem.
Union iof iA iand iB
The iunion iof ievents iM iand iA iis ithe iset iof iall isample ipoints iin ithe isample ispace ithat iare iin iMior
iA ior iboth.
The iunion iof ievents iM iand iA iis idenoted iMA. iOR iis ioften iused ito iindicate ithe iunion iof
itwoievents.
The iprobability ithat iM ior iA i(the iunion iof iM iand iA) iwill ioccur iisiP(MA)
= iP(M) i+ iP(A) i– iP(MA)
i
i i i i i i
.
1 Gina iFox ihas istarted iher iown icompany, iFoxy iShirts, iwhich imanufactures iimprinted ishirts
iforispecial ioccasions. iSince ishe ihas ijust ibegun ithis ioperation, ishe irents ithe iequipment ifrom
ia ilocal iprinting ishop iwhen inecessary. iThe icost iof iusing ithe iequipment iis i$350. iThe
imaterials iused iin ione ishirt icost i$8, iand iGina ican isell ithese ifor i$15 ieach.
(a) How imany ishirts imust iGina isell ito ibreak ieven?
(b) What iis ithe itotal irevenue ifor ithis?
Mark iyour ianswer icarefully. iPartial icredit iwill ibe iawarded ieither ipart-a ior ipart-bianswer
icorrectly iand ifull icredit iif iboth iparts iare ianswered icorrectly
Selectedi
Answer:
Part-a) i50 iand iPart-b) i750
f i = i 350 s i = i 15 v i = i8
Responsei f i = i 350 s i = i 15 v i = i8
Feedback: a) iBEP i = if/(s i − iv) i = i350/(15 i − i8) i = i50 iunits
b)Total irevenue = 50(15) = $750
If iGina isells i20 ishirts, iwhat iwill iher itotal irevenue ibe? iWhatiwill
iher itotal ivariable icost ibe?
c) iTotal irevenue i = i20(15) i = i$300
id))Total ivariable icost i = i20(8) i = i$160
2 i.
A icouple iof ientrepreneurial ibusiness istudents iat iFrostburg iState iUniversity idecided ito iput
itheir ieducation iinto ipractice iby ideveloping ia itutoring icompany ifor ibusiness istudents.
iWhileiprivate itutoring iwas ioffered, iit iwas idetermined ithat igroup itutoring ibefore itests iin ithe
ilarge istatistics iclasses iwould ibe imost ibeneficial. iThe istudents irented ia iroom iclose ito icampus
ifor
$300 ifor i3 ihours. iThey ideveloped ihandouts ibased ion ipast itests, iand ithese ihandouts
i(including icolor igraphs) icost i$5 ieach. iThe itutor iwas ipaid i$25 iper ihour, ifor ia itotal iof i$75
iforieach itutoring isession.
(a) If istudents iare icharged i$20 ito iattend ithe isession; ihow imany istudents imust ienroll ifor
itheicompany ito ibreak ieven?
(b) A isomewhat ismaller iroom iis iavailable ifor i$200 ifor i3 ihours. iThe icompany iis
iconsideringithis ipossibility. iHow iwould ithis iaffect ithe ibreak-even ipoint?
Mark iyour ianswer icarefully. iPartial icredit iwill ibe iawarded ieither ipart-a ior ipart-bianswer
icorrectly iand ifull icredit iif iboth iparts iare ianswered icorrectly
Part-a) iBEP i= i25 i Part-b) iBEP i= i18.33
Responsei a) i f i = i 300 i + i 75 i =
Feedback: i375 s i = i 20 iv i = i 5
BEP i = if/(s i– iv) i = i375/(20 i–
, BEP i = if/(s i − iv) i = i275/(20 i − i5) i =
i 1i8.333
3. What iis ithe iformula ifor ithe ibreak-even ipoint iof ia isimple iprofit imodel?
Fixed iCost i/ i(Selling iPrice iPer iUnit i- iVariable iCost iPer iUnit)
4.
Trying ivarious iapproaches iand ipicking ithe ione ithat iresults iin ithe ibest idecision iis icalled
the itrial-and-error imethod.
Question i5
Evaluating iall ipossible ivalues iof ia ivariable iin ia imodel iis icalled
Selected iAnswer: i complete ienumeration.
Question i6
Which iof ithe ifollowing iterms iis iinterchangeable iwith iquantitative ianalysis?
Selected iAnswer: management iscience
Question i7
The iwidespread iapplicability iof ioperations iresearch imethods ito ibusiness ifollowed
iwhichiwar?
Selected iAnswer: i World iWar iII
Question i8
Which iof ithe ifollowing itechniques iinvolves ithe iuse iof ioptimization imethods ito iprovide inewiand
ibetter iways ito ioperate ibased ion ispecific ibusiness iobjectives?
Selected iAnswer: i prescriptive ianalytics
Expressing iprofits ithrough ithe irelationship iamong iunit iprice, ifixed icosts, iand ivariable icosts iisian
iexample iof
Selected iAnswer: i a iquantitative ianalysis imodel.
Question i10
Which iof ithe ifollowing iis inot ione iof ithe isteps iin ithe iquantitative ianalysis iapproach?
Question i11
Which iof ithe ifollowing iis ia ipicture, idrawing, ior ichart iof ireality?
Question i12
,All iof ithe ifollowing iare ireal icomputer iapplications ithat iperform iquantitative ianalysis iexcept
QA i for i Windows
Question i13
Decision ivariables imay ialso ibe icalled iparameters.
Selected iAnswer: iFalse
Question i14
A icontrollable ivariable iis ialso icalled ia variable.
decision
Question i15
Models ican ihelp ius ianalyze ia iproblem iand isell ia idecision ito ithose iwho imust iimplement iit.
True
Question i16
Management isupport iand iuser iinvolvement iare inot iessential iin ithe
isuccessfuliimplementation iof iquantitative ianalysis iprojects.
Selected iAnswer: i False
Question i17
Interviews, istatistical isampling, iand icompany ireports iprovide iinput idata ifor
iquantitativeianalysis imodels.
True
Question i18
A imathematical imodel ishows ithe irelationship ibetween iquantifiable iand inon-
quantifiableiinformation.
Selected iAnswer: i False
Question i19
When ia iproblem iis idifficult ito iquantify, iit imay ibe inecessary ito idevelop iunspecific iobjectives.
Selected iAnswer: i False
Question i20
Business iAnalytics iis ia idata-driven iapproach ito idecision imaking ithat iallows icompanies
itoimake ibetter idecisions.
M i3
QU iE STION i 1
Which iof ithe ifollowing iis ia irequired icondition ifor ia idiscrete iprobability ifunction?
, D. i∑p(x) i= i1 ifor iall ivalues iof ix
5 ipoints
QU iE STION i 2
Assume iyou ihave iapplied ifor itwo ischolarships, ia iMerit ischolarship i(M) iand ian
iAthleticischolarship i(A). iThe iprobability ithat iyou ireceive ian iAthletic ischolarship iis i0.18. iThe
iprobability iof ireceiving iboth ischolarships iis i0.11. iThe iprobability iof igetting iat ileast ione iof
ithe ischolarships iis i0.3.
a). Are ievents iA iand iM imutually iexclusive? iWhy ior iwhy inot?
Two ievents iare isaid ito ibe imutually iexclusive iif ithe ievents ihave ino isample ipoints iin
icommon.iThat iis, itwo ievents iare imutually iexclusive iif, iwhen ione ievent ioccurs, ithe iother
icannot ioccuri(i.e. iP(MA) i= i0)
P(A iM) i =.3 i ≠ i 1 i and i P(A i ∩ i M) i =.11 i ≠ i 0 i A i and i M i are i not i mutually i exclusive.
b). Are ithe itwo ievents iA, iand iM, iindependent? iWhy ior iwhy
not?iTwo ievents iA iand iB iare isaid ito ibe iindependent iif iand
i
only iif:
i
P(A i∩ iM)P(A|B)
i=.11 i= iP(A) ior,P(A)
iequivalently,
iP i(M) i=.18 ix.P(B|A) i= iP(B)
i23 i= i.0414 i≠ iP(A i ∩ iM)
Therefore, iA iand iM iare inot iindependent.
.
Mark iyour ianswer icarefully. iPartial icredit iwill ibe iawarded ieither ipart-a ior ipart-
bianswer icorrectly iand ifull icredit iif iboth iparts iare ianswered icorrectly
Part ia) i No, ibecause iP(A i∩ iM) i≠ i0
Part ib) i No, ibecause iP(A i∩ iM) i≠ iP(A) iP(M)
QU iE STION i 3
Assume iyou ihave iapplied ifor itwo ischolarships, ia iMerit ischolarship i(M) iand ian iAthletic ischolarship
i(A).iThe iprobability ithat iyou ireceive ian iAthletic ischolarship iis i0.18. iThe iprobability iof ireceiving iboth
ischolarships iis i0.11. iThe iprobability iof igetting i at ileast ione iof ithe ischolarships iis i0.3.
a. What iis ithe iprobability ithat iyou iwill ireceive ia iMerit ischolarship? i**"at ileast" iis ianother
iwordifor ithe iunion iof itwo ievents. iThe iunion iformula ishould ihelp iyou iwith ithis iproblem.
Union iof iA iand iB
The iunion iof ievents iM iand iA iis ithe iset iof iall isample ipoints iin ithe isample ispace ithat iare iin iMior
iA ior iboth.
The iunion iof ievents iM iand iA iis idenoted iMA. iOR iis ioften iused ito iindicate ithe iunion iof
itwoievents.
The iprobability ithat iM ior iA i(the iunion iof iM iand iA) iwill ioccur iisiP(MA)
= iP(M) i+ iP(A) i– iP(MA)
i
