the air tran story: the merger and maximum point on profits-revenues graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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{bcp oq omugtpcjp bftf. jgp pbf frcap jvmftoacn ycnvfq* Puf OOO dfbcyogt {f qff
bftf qffmq pg df pbf utfavtqgt igt fopbft c mftkft "oi qgmfgjf oq ojpftfqpf`/ gt c
dcjhtvupa ionojk "{bfj jg qvopgtq ctf cyconcdnf. cq {opb Kfjftcn Mgpgtq* [bfjKM uvdnoan cjjgvjaf` opq {onnojkjfqq pg qfnn gii qgmf gi opq mgjf ngqojk
igvj`tofq. dcah oj 3??5q. {boab utg`vaf mcj atopoacn cvpgmgpoyf acqpojkq pbftf
{ftf jg dvftq# Pbf ncppft oq dcqf` gj tfagnnfapogj gi uvdnoqbf` tfugtpq `vtojk pbcp
pomf*/Pboq qbgvn` df agmuctf` pg pbf ktcub igt 3??6 {bfj Cot Ptcj {cq cdnf pg
tfugtp utgiopq {opb yft qmcnn tfyfjvfq* Pbf cjjvcn tfyfjvf igt 3??6 {cq gjn
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Ktg{pb `vtojk c qojknf fct
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Ktg{
pb`vtojkcqojknffct
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= -5*3;2r ( 324*53
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Tfyfjvfq-Ngqqfq
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-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
12/40
Uckf 34 gi05
$19;*;6; monnogj. dfp{ffj 65& pg 95& gi pbf tfyfjvf igt cj gjf svctpft oj 4552*
Qponn. Cot Ptcj agvn` jgp tfugtp c utgiop oj 4552*
Iokvtf 0< Pbf utgiopcdnf fct 3??6. {opb Puf O dfbcyogt tfyfcnf` d pbf qgno`
vu{ct` qnguojk nojf. oq agmuctf` {opb pbf Puf OOO dfbcyogt gdqftyf` oj 3??9.
3??;. cj` 4552 {opb cjjvcn ngqqfq* Fyfj {opb ktfcpn ojatfcqf` tfyfjvfq. cq
tfyfcnf` d pbf icap pbcp pbf `cpc igt 3??6-3??; ctf atg{`f` pgkfpbft jfct pbf
gtokoj. Cot Ptcj {cq vjcdnf pg tfugtp c utgiop oj 4552* "Pbf Puf OOO nojf igt 3??;
oq cj ojpftfqpojk iojcjaocn frcmunf gi c nojf {opb c jfkcpoyf qnguf {boab mchfq c
jfkcpoyf ojpftafup gj DGPB pbf utgiopq cj` pbf tfyfjvfq crfq* Mgqp Puf OOO nojfqmchf c ugqopoyf ojpftafup gj dgpb pbf crfq* / Ojqpfc` gi utgiopq oj`oacpf` d pbf
frptcugncpogj gi pbf Puf O nojf igt 3??6. op tfugtpf` opq bokbfqp ngqqfq. tfyfcnf` d
pbf p{g Puf OOO nojfq igt 4552* Oj gpbft {gt`q. pbf svc`tcjp igvt ktcub oq pg df
{bgnn cygo`f` {bfj {f agjqo`ft pbf avmvncpoyf `cpc "itgm svctpftn tfugtpq/ oj c
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"3??9. 3??;. 4552/
-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
13/40
Uckf 31 gi05
qojknf fct* Op mc df pbf utfavtqgt pg fopbft dcjhtvupa ionojk "oi jg gjf {cjpq pg
pchf gyft pbf agmucj/ gt c mftkft {opb c {onnojk qvopgt*
6* Puf OOO DfbcyogtMvnpo-fct Utgiopq-Tfyfjvfq Ktg{pb
Agjqo`ft jg{ pbf ignng{ojk ojpft-fct `cpc igt 455;-4535 itgm pbf 4535 Cjjvcn
Tfugtp* Pboq `cpc oq ungppf` oj Iokvtf 6 cj` tfyfcnq cj ojpftfqpojk yftqogj gi pbf
Puf OOO dfbcyogt frpfj`ojk gyft qfyftcn fctq*
_fct Tfyfjvfq. r$. monnogjq Utgiopq. $. monnogjq Agqpq "r/$. monnogjq
4535 493?*;34 12*601 4623*39?455? 4103*004 310*994 4459*;24552 4664*0;2 -499*110 4232*234455; 415?*?21 64*921 446;*1
[f qff c yft ojpftfqpojk ucppftj oj pbf pomf-fygnvpogj gi utgiopq cj` tfyfjvfq*
Pboq acj df `fqatodf` d pbtff qptcokbp nojf qfkmfjpq cnn {opb c jfkcpoyf qnguf*
Igt 455; cj` 4552< = -3*136r ( 15?4
Igt 4552 cj` 455?< = -3*136r ( 15?4
Igt 455? cj` 4535< = -5*106r ( ?01*01
Pbf tfyfjvfq ojatfcqf` dfp{ffj 455; cj` 4552 dvp pbf utgiopq `fatfcqf`qg
mvab pbcp CotPtcj capvcnn tfugtpf` c bvkf ngqq# Pboq oq {bcp {cq ancqqoiof` cq
Puf OOO dfbcyogt cj` oq oj`oacpf` d pbf nojf {opb pbf jfkcpoyf qnguf "b > 5. a : 5/*
Vqojk pbf gtmvncf koyfj fctnoft. igt pbf fsvcpogj gi c qptcokbp nojf agjjfapojk cjp{g ugojpq. {f kfp = -3*136r ( 15?4* Pbf cttg{ qbg{q pbf `otfapogj gi pomf*
Jfrp. tfyfjvfq `fatfcqf` dfp{ffj 4552 cj` 455? dvp jg{ CotPtcj tfugtpf` c joaf
utgiop* Pbf `cqbf` nojf. {opb pbf jfkcpoyf qnguf. oj`oacpfq pboq cj` pchfq vq pg pbf
ugojp cdgyf pbf tf` nojf* Pboq oq cj ojpftfqpojk yctocjp gi pbf Puf OOO dfbcyogt.
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
14/40
Uckf 30 gi05
{opb utgiopq ojatfcqojk {opb `fatfcqojk tfyfjvfq* "Pboq oq gdqftyf` {opb gpbft
agmucjofq cq {fnn. qff _cbgg `oqavqqf` oj Tfiq* X3-1]*/ Pbf fsvcpogj igt pbf jf{
Puf OOO nojf oq = -3*136r ( 15?4*
Jfrp. tfyfjvfq ojatfcqf` dfp{ffj 455? cj` 4535 dvp utgiopq `fatfcqf` gjaf ckcojdvp c ngqq {cq cygo`f`* Pboq pgg oq Puf OOO dfbcyogt. qomonct pg pbcp gdqftyf`
dfp{ffj 455; cj` 4552* Pbf fsvcpogj gi pboq nojf oq = -5*106r ( ?01*01*
Iokvtf 6< CotPtcj utgiopq-tfyfjvfq ktcub igt 455;-4535 qbg{ojk cj ojpftfqpojk
atoqq-atgqqojk Puf OOO dfbcyogt"gt c dcah cj` igtpb Cot Ptcj q{ggqbojk/* Pbf
bgto|gjpcn tf` nojf oq pbf r-croq* Gjf frufapq utgiopq pg ojatfcqf {opb ojatfcqojk
tfyfjvfq* Pboq oq pbf jgtmcn Pyuf Odfbcyogt "ugqopoyf ojpftafup gj tfyfjvfq-croq/gt Pyuf OO dfbcyogt "ugqopoyf ojpftafup gj pbf utgiopq-croq/ Dvp. {f cnqg qff pbf
guugqopf dfbcyogt {opb qfyftcn agmucjofq. cp nfcqp oj qgmf qopvcpogjq* Oi utgiopq
`fatfcqf {opb ojatfcqojk tfyfjvfq. gt ojatfcqf {opb `fatfcqojk tfyfjvfq "fq. op oq
ugqqodnf#/. {f bcyf Puf OOO dfbcyogt* Pboq oq {bcp {f qff bftf {opb Cot Ptcj*
-155
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Tfyfjvfq. r X$. monnogjq]
Utgiopq.X$.monnogjq]
Puf OOO mg`f455;-4535
-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
15/40
Uckf 36 gi05
9* Puf O. Puf OO. cj` Puf OOO DfbcyogtMvnpo-fct Utgiopq-Tfyfjvfq Ktg{pb
C qvaafqqivn agmucj mvqp tfugtp c utgiop fyft fct* D pbcp mfcqvtf. CotPtcj
bcq tfugtpf` c utgiop igt 2 gvp gi 35 tfafjp fctq. {opb c qmcnn ngqq oj 4553 cj` c
mvab dokkft ngqq oj 4552* Dvp pchf c actfivn nggh cp pbf utgiopq-tfyfjvfq ktcub oj
Iokvtf 9* Jg anfct ucppftj oq tfyfcnf`* Agjptcqp pboq {opb pbf utgiopq-tfyfjvfq ktcub
igt Qgvpb{fqp. igt pbf uftog` 3??4-4535. {boab tfyfcnq c anfct Puf O dfbcyogt*
Pboq oq utfqfjpf` oj Iokvtf 35* Bg{fyft. pbf ignng{ojk cnpftjcpoyf yof{ gi Cot
Ptcjq iojcjaocn uftigtmcjaf oq ugqqodnf oi {f okjgtf pbf ngqq igt 4552*
Iokvtf 9< Fttcpoa utgiopq-tfyfjvf ktcub igt CotPtcj igt pbf
pfj-fct uftog` itgm 4553-4535*
-155
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Tfyfjvfq. r X$. monnogjq]
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onnogjq]
-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
16/40
Uckf 39 gi05
Iokvtf ;< Cj cnpftjcpoyf yof{ gi pbf CotPtcj utgiopq-tfyfjvfq ktcub. oi {f
agmunfpfn okjgtf pbf 4552 `cpc*
Jg{ pbf utgiopq `cpc acj df `fqatodf` d p{g qptcokbp nojfq* Pbf tf` nojf. {opb pbffsvcpogj = br ( a = 5*540r ( ;2*6 qomun lgojq pbf 4551 cj` 455? `cpc* Pboq oq
Puf OO dfbcyogt "b : 5. a : 5/* Utgiopq ojatfcqf {opb ojatfcqojk tfyfjvfq dvp
vqvcnn cp c ng{ft tcpf pbcj c Puf O dfbcyogt "b : 5. a > 5/*
Pbf dnvf nojf oq pbf dfqp-iop nojf pbtgvkb pbf tfmcojojk `cpc ugojpq. {opb pbf
fsvcpogj = 5*5430r30*02 = 5*5430 "r9;9*4/* Pboq oq anfctn c Puf O
dfbcyogt* Pbf nojf mchfq c ugqopoyf ojpftafup gi r = r5 = -a'b = 30*02'5*5430 =
$9;9*4 monnogj gj pbf tfyfjvfq-croq* Pbf `cpc igt 4553 agjiotmq pboq avp gii qojaf
CotPtcj bc` c qmcnn ngqq {opb tfyfjvfq gi $996*390 monnogj* Dfgj` pboq avp-gii.gt dtfchfyfj. tfyfjvfq. CotPtcj {cq cdnf pg tfugtp c qmcnn utgiop "mvab nfqq pbcj
{opb pbf Puf OO qopvcpogj. pbf `oiiftfjaf dfojk pbf nctkf ugqopoyf ojpftafup/*
-05
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5
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395
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5 655 3555 3655 4555 4655 1555 1655
Tfyfjvfq. r X$. monnogjq]
Utgiopq.X$.monnog
jq] Puf OO
= 5*540r ( ;2*6
Puf O = 5*5430r - 30*6
= 5*5430 "r
9;9*4/
-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
17/40
Uckf 3; gi05
;* Ptcjqopogjq oj Utgiopq-Tfyfjvfq Ktg{pb
Pbf Cot Ptcj Utgiopq-Tfyfjvfq `cpc igt pbf fjpotf qorpffj "39/ fct uftog` itgm
3??1 pg 4535 acj df `fqatodf`. cq qffj oj Iokvtf 2. d c qftofq gi qptcokbp nojf
qfkmfjpq {boab tfyfcn pbf ptcjqopogjq dfp{ffj pbf pbtff Pufq gi dfbcyogt
qvkkfqpf` d pbf qomunf nojfct utgiopq-tfyfjvfq nc{*
Iokvtf 2< Pbf utgiopq-tfyfjvfq ktcub igt CotPtcj igt pbf qorpffj fct "39/ uftog`
3??6-4535* Cot Ptcj tfugtpf` c utgiop igt gjn 4 gvp gi pbf 9 c``opogjcn fctq "oj
4555 cj` 3??6/* Pboq 39-fct ktcub tfyfcnq dgpb pbf Puf O "dgpb pbf dnvf cj` tf`
nojfq {opb c ugqopoyf qnguf/ cj` pbf Puf OOO dfbcyogt {opb cj ojpftyfjojk Puf OOqbg{j d pbf `cqbf` nojf* Pbf qptcokbp nojf qfkmfjpq tfyfcn pbf kfjftcn ptfj`q*
Pboq nfc`q vq pg pbf ojptokvojk ugqqodonop gi c qmggpb jgjnojfct avtyf. {opb c
mcromvm ugojp. pg `fqatodf pbf qcmf `cpc. cq qvkkfqpf` d pbf `cqbf` avtyfq
"JGP `ftoyf` itgm cj mcpbfmcpoacn acnavncpogjq/ oj Iokvtf ?* Pbf igvt ugojpq
-155
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Tfyfjvfq. r X$. monnogjq]
Utgiopq.X$.monn
ogjq]
Puf O
Puf OO
Puf OOO
-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
18/40
Uckf 32 gi05
cngjk pbf avtyf. ucqp pbf mcromvm. ctf igt 455;-4535 {boab nf` pg pbf ojpftfqpojk
atoqq-atgqqojk Puf OOO dfbcyogt `oqavqqf` fctnoft*
2* Mcromvm Ugojp Utgiopq-Tfyfjvfq Ktcub
Iokvtf ?< Ugqqodnf cuufctcjaf gi c mcromvm ugojp gj pbf utgiopq-tfyfjvfq ktcub
igt CotPtcj* Uftbcuq. pboq {cq utfavtqgt pg pbf casvoqopogj gi Cot Ptcj* C
agmucj acjjgp agjpojvf pg guftcpf igt ngjk oj pbf Puf OOO mg`f {opb utgiopq
`fatfcqojk cq tfyfjvfq ojatfcqf. gt yoaf yftqc* "Oj pbf acqf gi Kfjftcn Mgpgtq.
{bftf c qomonct Puf OOO mg`f {cq gdqftyf` gyft qfyftcn fctq. op fyfjpvcnn nf` pgopq boqpgtoa dcjhtvupa ionojk oj Lvjf 455?*/ Jgpoaf bg{ `oiiftfjp agjanvqogjq ctf
uftmoppf` d pbf 35-fct `cpc cj` pbf 39-fct `cpc* Pbf icnnojk uctp gi pbf avtyf
acj df fjyoqogjf` {opb pbf 35-fct `cpc dvp pbf toqojk uctp oq gjn tfyfcnf` oi {f
agjqo`ft pbf 39-fct `cpc* Puf OOO dfbcyogt oq cn{cq utfaf`f` d Puf O cj`'gt
Puf OO* C toqf cn{cq utfaf`fq c icnn* Bfjaf. pbf Puf OOO dfbcyogt vqvcnn
-155
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Tfyfjvfq. r X$. monnogjq]
Utgiopq.X$.monnogjq]
-
7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
19/40
Uckf 3? gi05
qvkkfqpq pbf froqpfjaf gi cj fctnoft Puf O dfbcyogt cj` cnqg c mcromvm ugojp gj
pbf utgiopq-tfyfjvfq ktcub* Pbf kfjftcn fsvcpogj. = mrj Xf-cr '"3 ( df-cr/ ] ( a.
gt opq qomunoiof` yftqogj. = mrjf-cr ( a. {opb cuutgutocpf ycnvfq gi pbf agjqpcjpq
m. j. c. d cj` a. acj df vqf` pg mg`fn pboq gyftcnn dfbcyogt* Pbf ivj`cmfjpcn
qokjoioacjaf gi pboq mcpbfmcpoacn fsvcpogj oq `oqavqqf` dtofin oj ?*
Iokvtf 35< Pbf utgiopq-tfyfjvfq ktcub igt Qgvpb{fqp Cotnojfq. igt
pbf uftog` 3??4-4555* Utgiopq ojatfcqf {opb ojatfcqojk tfyfjvfq*
C joaf vu{ct` Puf O ptfj` oq tfyfcnf` d pboq `cpc* Pbf fsvcpogj
gi pbf dfqp-iop nojf pbtgvkb pbfqf ugojpq oq = br ( a = b "r r5/ = 5*341r5*303
= 5*341 "r3*360/ {opb pbf nojfct tfktfqqogj agfiioaofjp bcyojk c yft bokb ycnvf
gi t4 = 5*?16* Cppfjpogj qbgvn` cnqg df acnnf` pg pbf jfctn UFTIFAP utgiopq-
tfyfjvfq ktcub igt Cuunf Oja*. {opb t4 = 5*???26. tfugtpf` oj pbf ctpoanfq aopf` oj
pbf tfiftfjafq8 qff Pbf Uftifap Cuunf*
Oj qvmmct. c actfivn qpv` gi pbf boqpgtoacn utgiopq-tfyfjvfq `cpc igt CotPtcj. oj
pbf 35-fct uftog` ommf`ocpfn utfaf`ojk opq casvoqopogj d Qgvpb{fqp. tfyfcnq
ojpftfqpojk abcnnfjkfq cbfc` igt pbf jf{ agmucj* Agqpq bcyf anfctn dffj toqojk
-5*4
5
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5*5 3*5 4*5 1*5 0*5 6*5 9*5 ;*5 2*5
Tfyfjvfq. r X$. donnogjq]
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donnogjq]
Puf O dfbcyogt = 5*341r 5*303
= 5*341 "r 3*360/t4 = 5*?19
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
20/40
Uckf 45 gi05
cj` utgiopq `fatfcqojk. fct-cipft-fct. cq tfyfcnf` d pbf `fatfcqojk qngufq b cj`
ojatfcqojk ycnvfq gi pbf ojpftafupq "dtfchfyfj tfyfjvf/ mc`f gj pbf tfyfjvf croq*
_fct Tfyfjvfq. r$. donnogjq
Utgiopq. $. donnogjq
Agqpq "r/$. donnogjq
4535 4*94 5*5126 4*623455? 4*10 -5*4991 4*23?4552 4*66 5*310; 4*45;455; 4*13 5*564; 4*46;4559 3*2? 5*530; 3*2;;4556 3*06 5*553; 3*00?4550 3*50 5*5341 3*54?4551 5*?4 5*3556 5*232
Oi dvqojfqq cj` iojcjaf mclgtq utfift JGP pg vqf pbf `fqokjcpogj Agqpq
igt pbf svcjpopy oj pbf ncqp agnvmj. {f acj acnn op pbf {gth ivjapogj gi pbf
agmucjy8 qff `oqavqqogj gi Fojqpfojq ubgpgfnfaptoa nc{ oj 35*
Pboq mc cnqg df cuutfaocpf` d agjqo`ftojk pbf agqpq oj pbf ncqp agnvmj gi pbf
pcdnfq. {boab {ftf agmuvpf` itgm pbf dcqoa fsvcpogj Utgiopq = TfyfjvfqAgqpq
gt U = TA* Pbf mojo-pcdnf cdgyf agjqo`ftq pbf `cpc igt 4551-4535*
Oj 4551. {opb tfyfjvfq gi cnmgqp $3 donnogj "$5*?4 D. frcapn/ pbf utgiopq {ftf
$5*35 donnogj. {boab mfcjq pbf agqpq {ftf cdgvp $5*? D "$5*24 D. frcapn/* Oj
4559. {bfj tfyfjvfq bc` `gvdnf` pg jfctn $3*2? donnogj. utgiopq {ftf capvcnnng{ft pbcj oj 4551. {boab mfcjq pbf agqpq koyfj oj pbf ncqp agnvmj bc` mgtf pbcj
`gvdnf`* Oj 4535. {opb c jfct ptounojk gi tfyfjvfq pg $4*94 donnogj. pbf utgiopq {ftf
ckcoj ng{ft pbcj oj 4551* Pbf agqpq bc` mgtf pbcj ptounf` agmuctf` pg 4551* Oj
4552. pbf fct gi mcromvm utgiopq. pbf tfyfjvfq {ftf cdgvp 4*6 pomfq pbf tfyfjvfq
oj 4551 dvp pbf utgiopq {fjp vu gjn d cdgvp 16& "itgm $355 monnogj pg $316
monnogj/* C mgtf `fpconf` cjcnqoq gi pbf agqpq-tfyfjvfq tfncpogj oq utgyo`f` oj pbf
qfuctcpfn oj pbf ctpoanf gj Qgvpb{fqp Cotnojfq. qff dodnogktcub*
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
21/40
Uckf 43 gi05
Iokvtf 33< Avmvncpoyf Tfyfjvfq yftqvq Utgiopq igt Cot Ptcj "3??1-4535/*Ojpftfqpojkn. cipft pbf ufch oj 3??6. pbf avmvncpoyf utgiopq jfyft ivnn tfagyftf`*
Pbf dtofi `oqavqqogj oj ? cj` 35 oq dfojk giiftf` bftf igt agmunfpfjfqq*
Ivtpbft `fpconq mc df igvj` oj pbf ctpoanfq aopf` oj pbf dodnogktcub*
?* Dtofi @oqavqqogj
Pbf qomunfqp fsvcpogj igt c qptcokbp nojf. ucqqojk pbtgvkb pbf gtokoj "{f okjgtf pbf
ojpftafup a igt pbf mgmfjp/. oq = mr cj` pbf qomunfqp fsvcpogj igt c avtyf {opb c
abcjkojk qnguf oq = mrj {bftf j = 3 koyfq pbf qptcokbp nojf cj` j : 3 ofn`ojk c
avtyf {opb ojatfcqojk qnguf "caafnftcpogj gi / cj` j > 3 ofn` c avtyf {opb
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355
365
5 4.655 6.555 ;.655 35.555 34.655 36.555 3;.655 45.555
Avmvncpoyf Tfyfjvfq. r X$. donnogjq]Qpctpojk 3??1
AvmvncpoyfUtgiopq.X$.d
onnogjq]
Qpctpojk3??1
4535
455;3??6
3???
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
22/40
Uckf 44 gi05
`fatfcqojk qnguf "`fafnftcpogj gi /. qff Iokvtf 34* Pboq oq acnnf` pbf ug{ft nc{
cj` j oq acnnf` pbf ug{ft nc{ oj`fr* Itoapogjcn. gt cot. tfqoqpcjaf "gt pbf `tck/.
fruftofjaf` d c mgyojk gdlfap qvab cq c kgni dcnn. act. ptvah. cotatcip. gt c tgahfp
oq gipfj frutfqqf` vqojk pbf ug{ft nc{*
Iokvtf 34< Qomunf onnvqptcpogj gi pbf ug{ft-nc{ dfbcyogt. = mrj igt pbf pbtff
acqfq. j = 3 "nojfct nc{/. j :3 ofn`ojk caafnftcpojk ktg{pb gi utgiopq {opb
ojatfcqojk tfyfjvfq cj` j >3 ofn`ojk `fafnftcpojk ktg{pb gi utgiopq {opb
ojatfcqojk tfyfjvfq* Oj cnn pbtff acqfq. pbftf oq JG nomop pg pbf mcromvm tfyfjvfq
gt utgiopq* Pboq qopvcpogj oq aftpcojn ict mgtf `fqotcdnf pbcj pbf qopvcpogj {bftf c
mcromvm ugojp cuufctq gj pbf utgiopq-tfyfjvf avtyf "qff Iokvtf 31/*
Pbf ktcub gi quff` yftqvq pomf. oj tgc` pfqpq tgvpojfn uftigtmf` pg cqqfqq pbf
uftigtmcjaf gi yfboanfq. acj cnqg df `fqatodf` d c ug{ft nc{* "O bcyf agjiotmf`
pboq {opb qfyftcn yfboanf tgc` pfqp `cpc*/ Pbf caafnftcpogj c = y'p oq pbf qnguf gi
pbf ktcub gi quff` "gt mgtf agttfapn yfngaop. bfjaf pbf qmdgn y/ yftqvq pomf p*
Tgc` pfqpq qbg{ pbcp pbf caafnftcpogj oq jgp c agjqpcjp dvp capvcnn `fatfcqfq {opb
pomf "gt ojatfcqojk quff`/* Pboq oq `vf pg pbf cot tfqoqpcjaf "cftg`jcmoa `tck/ lvqp
5*55
5*65
3*55
3*65
4*55
4*65
1*55
1*65
5*5 6*5 35*5 36*5 45*5 46*5
= 5*3rm = 5*3 cj` j = 3
= 5*3r3*36
m = 5*3 cj` j = 3*36
= 5*3r5*26
m = 5*3 cj` j = 5*26
Tfyfjvfq r
Utgiopq.
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 41 gi05
mfjpogjf` cj` koyfq pbf jgjnojfct ug{ft nc{ avtyf igt y-p tfncpogj* Mcj gpbft
frcmunfq gi qvab jgjnojfct nc{q acj df aopf`*
Iokvtf 31< Onnvqptcpogj gi pbf pbtff qufaocn acqfq gi = mrjf-cr. {boab oq pbf
qomunfqp igtm gi pbf ug{ft-frugjfjpocn nc{< pbf nojfct nc{ = 5*6r "j = 3. c = 5/.
pbf ug{ft nc{ = 5*9r5*9; "c = 5/ cj` pbf ug{ft-frugjfjpocn. = 1r5*9;f-5*346r* Pbf
mcromvm ugojp gaavtq {bfj r = j'c = 5*9;'5*346 = 6*19* Igt j = 5. pbf nc{
dfagmfq = mf-cr. c uvtf frugjfjpocn dfbcyogt "frcmunf. tc`ogcapoyf fac/*
Bg{fyft. pbf nojfct cj` jgjnojfct nc{q `g jgp tfyfcn c mcromvm ugojp* Cq r
ojatfcqfq ojatfcqfq. oj`fiojopfn. {opb gjn pbf tcpf gi ojatfcqf 'r. gt `'`r
caagt`ojk pg pbf acnavnvq jgpcpogj. dfojk `oapcpf` d pbf frcap mcpbfmcpoacn nc{*
Gjf {gvn` nohf utgiopq pg ojatfcqf cq tfyfjvfq ojatfcqf* Fyfj dfppft. oi utgiopq
{gvn` ojatfcqf cp cj caafnftcpojk tcpf* Bg{fyft. cq {f qff bftf {opb Qgvpb{fqp
Cotnojfq. {boab bcq tfugtpf` c utgiop igt fyft qojknf fct igt 1? fctq. {f `g jgp
5
3
4
1
0
6
9
;
2
5 6 35 36 45 46 15 16
Utg
iopq.
Tfyfjvfq. r X$. donnogjq]
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
24/40
Uckf 40 gi05
qff cj caafnftcpogj oj pbf ktg{pb gi utgiopq {opb ojatfcqojk tfyfjvfq* Cp dfqp {f
qff c nojfct nc{ "Iokvtf 35/* Pboq oq cnqg ptvf oi {f qpv` pbf `cpc igt mcj gpbft
agmucjofq "qff `oqavqqogj gi Cuunf oj Tfiq* X3] cj` X4]/* Pbftf oq jg agmucj
pbcp O cm c{ctf gi. dcqf` gj mcj qvab qpv`ofq gi bvj`tf`q gi agmucjofq qojaf
3??2. pbcp bcq agjqoqpfjpn qbg{j cj caafnftcpogj "j : 3/. igt c qvqpcojf` uftog` gipomf. oj pbf utgiopq-tfyfjvf qucaf*
Qbgvn` {f frufap pg qff c mcromvm ugojp gj pbf utgiopq-tfyfjvf ktcub7 [bonf op
oq fcq pg qufavncpf cdgvp pboq ugojp. {b {gvn` gjf frufap pg qff c mcromvm
ugojp7 Pboq oq qg agvjpftojpvopoyf pg pbf {bgnf o`fc gi cn{cq ptojk pg mcromo|f
utgiopq* Cncq. gyft pboq ucqp mgjpb "qojaf pbf Icafdggh OUG/. O ioj` pbcp mcj tfcn
{gtn` agmucjofq `g qbg{ c mcromvm ugojp gj pbfot utgiopq-tfyfjvfq ktcub* Cot
Ptcj "cj` cnqg Qgvpb{fqp Cotnojfq. pg df uvdnoqbf` qfuctcpfn/ ctf lvqp pbf ncpfqp
frcmunfq gi pboq dfbcyogt* Pbf gpbftq ctf Igt` Mgpgt Agmucj. Yfto|gj. _cbgg.
cj` Htgkft* Fcab gjf gi pbfqf agmucjofq oq qffmojkn utgiopcdnf dvp fcab gjf oq
qptvkknojk*
Uftbcuq. pbftf oq qgmf cq fp vj`oqagyftf` jcpvtcn nc{ "gi dfbcyogtcn
fagjgmoaq cj` iojcjaf/ pbcp oq tfqugjqodnf igt pbf mcromvm ugojp* Cnqg. pbojh
cdgvp pbf oj`fiojopf ojatfcqf oj utgiopq {opb ojatfcqojk tfyfjvfq* Oj mcpbfmcpoaq.
{f acj qc. cj` {f gipfj `g. cq r . * Pboq mokbp df ptvf cq ngjk cq {f
ctf `fcnojk {opb uvtfn agjafupvcn mcpbfmcpoacn fjpopofq* Jg{. cuun op pg iojcjafgt mgjf cj` {f ctf `fcnojk {opb cj vjpfjcdnf `gvdnf ojiojop gi qgtpq. oqjp op7
Bg{ acj ojiojopf tfyfjvfq ofn` ojiojopf utgiopq7 Vjnfqq. gi agvtqf. agqpq kg pg
|ftg# Mc df jg{ {f bcyf qpvmdnf` vugj c qomunf "mcpbfmcpoacn7/ fruncjcpogj
igt pbf mcromvm ugojp oj pbf utgiopq-tfyfjvfq ktcub*
Qg. jg{. kgojk c qpfu ivtpbft. pbf qomunfqp fsvcpogj igt c avtyf {opb c mcromvm
ugojp oq = mrjf-cr* Pboq oq acnnf` pbf ug{ft-frugjfjpocn nc{ cj` oq pbf qomunf
utg`vap gi pbf uvtfn toqojk ug{ft nc{ " = mrj/ cj` uvtfn icnnojk frugjfjpocn
`fac nc{ " = f-cr
/* Oi c = 5. pbf mcromvm ugojp `oqcuufctq cj` {f kfp pbf ug{ftnc{* Oi c = 5 cj` j = 3. {f kfp pbf qomunf nojfct nc{ gt qptcokbp nojf* Dvp. cncq.
qptcokbp nojfq ctf joaf dvp pbf `g jgp cn{cq ucqq pbtgvkb pbf gtokoj* Bfjaf. {f
mvqp c`` pbf jgj|ftg agjqpcjp a pg gvt fsvcpogjq* Cq qffj bftf. pbf jgj|ftg a oj
pbf utgiopq-tfyfjvfq ktcub oq `vf pg pbf iorf` agqpq* Pbf kfjftcn fsvcpogj igt c
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 46 gi05
qptcokbp nojf oq = br ( a* Qvab c jgj|ftg ojpftafup cuufctq oj qgmf {fnn hjg{j
ubqoacn nc{q. fqufaocnn Fojqpfojq ubgpgfnfaptoa nc{. pg df `oqavqqf` qbgtpn*
Bg{fyft. ojqpfc` gi pbf qomunft = mrjf-cr. op oq mgtf cuufcnojk "cp nfcqp
ojpfnnfapvcnn qufchojk/ pg agjqo`ft pbf qnokbpn mg`oiof` ug{ft-frugjfjpocnfsvcpogj = mrj Xf-cr '"3 ( df-cr/ ] qojaf pboq oq jgpbojk mgtf pbcj pbf kfjftcno|f`
qpcpfmfjp gi pbf icmgvq fsvcpogj itgm dncahdg` tc`ocpogj. iotqp `ftoyf` d Mcr
Uncjah oj @fafmdft 3?55* Uncjahq gtokojcn fsvcpogj acj df {toppfj cq
v = "24'a1/ V
{bftf. V = X f-'hP '"3f-'hP/ ]
cj`. = b
koyojk. v = "2b'a1/1 X f-'hP '"3f-'hP/ ] "3/
[f `g jgp bcyf pg vj`ftqpcj` fyftpbojk cdgvp fsvcpogj 3 "fqufaocnn cnn pbf
qvdpnfpofq gi pbf ubqoaq pbcp nf` pg pbf `oqagyft gi pboq nc{/ frafup pg jgpf pbcp pbf
itfsvfja oq gvt yctocdnf r cj` pbf tc`ocpogj fjftk `fjqop v oq gvt yctocdnf *
Pbf itfsvfja oq tcoqf` pg pbf ug{ft 1 {boab oq pg df tfuncaf` d pbf kfjftcn
ug{ft nc{ oj`fr j* Pbf frugjfjpocn icapgt {opboj pbf qsvctf dtcahfpq oq fcqon
tfagkjo|f`* Oj pbf gtokojcn Uncjah fsvcpogj c = b'hP "{bftf P oq pbf pfmuftcpvtf
cj` h oq c agjqpcjp. acnnf` pbf Dgnp|mcjj agjqpcjp/* Pbf agjqpcjp m {boab utfaf`fqcnn oq koyfj d "2b'a
1/* Oj Uncjahq pbfgta oq pbf quff` gi nokbp cj` b oq cjgpbft
vjoyftqcn agjqpcjp {boab oq jg{ acnnf` pbf Uncjah agjqpcjp* "Uncjah gjn vqfq pbf
qmdgn b. oj boq @fafmdft 3?55 ucuft. {opbgvp koyojk op c jcmf*/
Pboq mg`oiof` igtm gi pbf ug{ft-frugjfjpocn fsvcpogj oq utfifttf` qojaf {f acj
tfc`on ftoyf Uncjahq fsvcpogj vqojk pbf qcmf qpcpoqpoacn ctkvmfjpq pbcp Uncjah
vqf` oj 3?55 cj` cuun op ojqpfc` pg pbf utgdnfm gi utgiopq gt tfyfjvfq kfp
`oqptodvpf` cmgjk mcj `oiiftfjp utg`vapq pbcp c agmucj utg`vafq cj` qfnnq*
Pbvq. pbf ug{ft-frugjfjpocn fsvcpogj = mrj Xf-cr'"3 ( df-cr/] ( a oq pbf qomunfqp
mcpbfmcpoacn nc{ tfncpojk r cj` {boab cnqg tfyfcnq c mcromvm ugojp* Pbf
qokjoioacjaf gi pboq nc{ mc df vj`ftqpgg` svopf qomun. cq ignng{q. d agjqo`ftojk
yctogvq qufaocn acqfq*
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 49 gi05
Nojfct nc{< Igt j = 3. cj` c = d = 5. pbf ug{ft-frugjfjpocn nc{ tf`vafq pg pbf
nojfct nc{ = mr ( a*
Ug{ft nc{< Igt c = 5 {f kfp pbf qomunf ug{ft nc{. = Mrj. {bftf M = m'"3(d/
oq c jf{ agjqpcjp pbcp tfuncafq m cj` cdqgtdq pbf jgj|ftg d oj pbf `fjgmojcpgt* Ojpboq acqf. pbftf oq JG mcromvm ugojp* Pbf `ftoycpoyf `'`r = j"'r/ oq jgj|ftg igt
cnn ycnvfq gi r* Bfjaf. pbf utgiopq {onn ojatfcqf oj`fiojopfn {opbgvp nomop. {opb
ojatfcqojk tfyfjvfq r fopbft cp cj caafnftcpojk tcpf "igt j : 3/ gt cp c `fafnftcpojk
tcpf "igt j > 3/ {opb ojatfcqojk tfyfjvfq "qff Iokvtf 34/* Igt j = 5. {f kfp uvtf
frugjfjpocn dfbcyogt "f*k* tc`ogcapoyf `fac. abctkojk gi dcppftofq. fpa*/
Ug{ft-frugjfjpocn nc{< C mcromvm ugojp cuufctq gjn {bfj c : 5. bg{fyft.
qmcnn* Pboq acj df cuutfaocpf` d agjqo`ftojk pbf qomunft acqf gi d = 5 cj` a = 5.
igt {boab = mrj
f-cr
* Pbf `ftoycpoyf `'`r = "j- cr/"'r/* Bfjaf. pbftf oq cmcromvm ugojp gj pbf ktcub cp r = j'c* Igt r > j'c pbf `ftoycpoyf `'`r : 5 cj`
ojatfcqfq {opb ojatfcqojk r* Igt r : j'c. pbf `ftoycpoyf `'`r oq jfkcpoyf cj`
`fatfcqfq {opb ojatfcqojk r* Pboq oq pbf puf gi dfbcyogt pbcp {f ctf {opjfqqojk
{opb Cot Ptcj "qff qabfmcpoa ktcubq oj Iokvtfq ? cj` 31/*
Pboq qomunf jgjnojfct Uncjah fsvcpogj. {opb c mcromvm ugojp. mc df vqf` pg
fruncoj pbf cuufctcjaf gi pbf mcromvm ugojp gj pbf utgiopq-tfyfjvfq ktcub igt
Qgvpb{fqp Cotnojfq* Gt. gjf mokbp pbojh oj pftmq gi pbf Mcr{fnn-Dgnp|mcjj puf
gi `oqptodvpogj oj pbf iojcjaocn cj` fagjgmoa {gtn`* Frcapn. qomonct gdqftycpogjq.tfkct`ojk pbf mcromvm ugojp. bcyf cnqg dffj mc`f "qojaf O dfkcj pboq tfafjp qpv`
cipft pbf `oqcuugojpojk Icafdggh OUG gj Ito`c Mc 32. 4534/ {opb qfyftcn
agmucjofq. mgqp jgpcdn Igt` Mgpgt Agmucj* Pbf Igt` `cpc tfyfcnq c mcromvm
ugojp. nohf {f qff bftf. ckcoj {opb c ngp gi qacppft*
Oj mcj {cq. dgpb Igt` cj` Qgvpb{fqp Cotnojfq ctf qomonct* Pbf Qgvpb{fqp `cpc oq
dfojk `oqavqqf` qfuctcpfn oj mgtf `fpcon* Dgpb pbfqf agmucjofq ctf avttfjpn
utgiopcdnf cj` cuufct pg df `gojk svopf {fnn* Bg{fyft. pbf ctf jgp cdnf pg tfugtp
agjqoqpfjpn bokb nfyfn gi utgiopq* Pbftf ctf pgg mcj {on` invapvcpogjq* Cnqg. pbf
jfkcpoyf "Puf OOO/ tfncpogj fqpcdnoqbf` "igt Cot Ptcj. cq `oqavqqf` bftf. cj` cnqg
Qgvpb{fqp. qojaf 455;/ dfp{ffj utgiopq cj` tfyfjvfq oq c acvqf igt qgmf agjaftj*
Pboq ugojp bcq dffj `oqavqqf` oj mgtf `fpcon oj Tfi* X3]* Mcj gpbft agmucjofq.
jgpcdn Igt`. Yfto|gj. _cbgg. cj` Htgkft. cnqg tfyfcn pboq pgroa Puf OOO
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 4; gi05
dfbcyogt* Pboq qffmq pg df c utfavtqgt pg agmucj tfugtpojk c agjpojvf` ngqqfq
fyfj cq tfyfjvfq ojatfcqf gt. cq {opb KM. pbf ionojk gi dcjhtvupa cipft c ngjk
uftog` qufjp oj pbf Puf OOO mg`f. gt. cq {opb Cot Ptcj. dfagmojk c pctkfp igt
mftkft'casvoqopogj* "C `oqavqqogj gi pbf gn` KM iojcjaocn `cpc. itgm 3??3 pg
4552. dfigtf pbf dcjhtvupa ionojk oj Lvjf 455? {onn df utfqfjpf` qfuctcpfn*/
Pboq oq {bcp dgpb Igt` cj` Qgvpb{fqp acj nfctj itgm pbf gn` KM* Puf OOO
dfbcyogt oq pbf tfaouf igt fyfjpvcn iconvtf cj` qbgvn` df tfyftqf` cp pbf fctnofqp*
bppu
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 42 gi05
35* Fojqpfojq Ubgpgfnfaptoa Nc{
cj` pbf Dvqojfqq [gtn`
Cnqg Nfkfj`tfq mfpbg` cj` Monnohcjq mfpbg` pg
`fpftmojf pbf fsvcpogj gi pbf qptcokbp nojf
Iojcnn. nfp vq dtofin oqavqq Fojqpfojq ubgpgfnfaptoa nc{ qojaf. cq {f {onn qff
bftf. op utgyo`fq c dfcvpoivn fruncjcpogj igt pbf nojfct nc{ = br (a pbcp {f
gdqftyf bftf oj pbf iojcjaocn {gtn`* Oj ubqoaq. {f bcyf qgmfpbojk acnnf` pbf
ubgpgfnfaptoa fiifap* Mg`ftj ubgpgafnnq. {boab {f ioj` cnn ctgvj` vq. {gth gj pboq
utojaounf* [bfj nokbp qbojfq gj pbf qvticaf gi qgmf mfpcnq op flfapq fnfaptgjq*
Pbfqf ctf pbfj agnnfapf` cj` cnng{f` pg ucqq pbtgvkb cj fnfaptoacn aotavop oj pbf
ubgpgafnnq* Aftpcoj omugtpcjp cqufapq gi ubgpgfnfaptoaop {ftf jgp {fnn vj`ftqpgg`
dcah oj 3?56 cj` uv||nf` ubqoaoqpq* Fojqpfoj capvcnn kgp boq Jgdfn Uto|f igt
fruncojojk bg{ pbf ubgpgfnfaptoa utgafqq {gthq* "Pbf Jgdfn Agmmoppff ifnp pbcp
boq pbfgt gi tfncpoyop {cq pgg agjptgyftqocn*/ Pbf fruncjcpogj oq yft qomunf*
Iotqp. Fojqpfoj qbg{q pbcp nokbp acj df omckojf` cq dfojk mc`f vu gi moatgqaguoa
uctpoanfq acnnf` ubgpgjq* "Fojqpfoj cttoyfq cp pboq agjanvqogj d agjqo`ftojk c
utguftp acnnf` pbf fjptgu gi tc`ocpogj* Pbf frutfqqogj igt fjptgu oq cnqg pbfqpctpojk ugojp igt Uncjah oj boq `fyfngumfjp gi pbf svcjpvm pbfgt*/ Pboq {cq c
tfygnvpogjct agjafup dcah oj 3?56 qojaf nokbp {cq kfjftcnn caafupf` cq dfojk c
{cyf* Ubfjgmfjc nohf ojpftiftfjaf cj` `oiitcapogj gi nokbp agvn` gjn df fruncojf`
vqojk pbf {cyf o`fc* Pbf {cyf pbfgt kgp ivtpbft qvuugtp {bfj Mcr{fnn
`fyfnguf` boq pbfgt gi fnfaptgmckjfpoqm {boab utf`oapf` pbf froqpfjaf gi {cyfq.
acnnf` fnfaptgmckjfpoa {cyfq. cnn gi {boab ptcyfn cp pbf quff` gi nokbp* Pboq nf` pg
pbf "tfygnvpogjct cj` ojpfnnfapvcnn unfcqojk/ o`fc pbcp nokbp opqfni mc df c {cyf
gi fnfaptgmckjfpoa gtokoj* Mcr{fnnq pbfgt cnqg utf`oapf` pbf froqpfjaf gi pbf
fjpotf fnfaptgmckjfpoa qufaptvm cj` nf` pg pbf ojyfjpogj gi tc`og {cyfq.
pfnfktcub. PY. tc`ct. mg`ftj afnn ubgjfq. KUQ fpa*
Pbf gvjk Fojqpfoj {cq pbvq `fiojk agjyfjpogjcn {oq`gm cj` c`ygacpojk c yft
dgn` o`fc* "Bf {oqfn acnnq op c bfvtoqpoa yof{ugojp igt nokbp#/ Jf{pgj omckojf`
nokbp pg df mc`f vu gi uctpoanfq "pbfj acnnf` agtuvqanfq/. fcab bcyojk c iorf`
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 4? gi05
mgmfjpvm my "m oq pbf mcqq gi fcab uctpoanf cj` y opq quff` gt yfngaop/* Pbf
agngt nokbp `fufj`q gj pbf mgmfjpvm gi opq uctpoanfq* Oj quopf giJf{pgjq
ptfmfj`gvq utfqpokf. pbf agtuvqavnct pbfgt gi nokbp {cq cdcj`gjf` qojaf op {cq
jgp qvuugtpf` d fruftomfjpq* Qg. Fojqpfoj tfojptg`vaf` pbf uctpoanf yof{ {opb c
jf{ p{oqp* Ojqpfc` gi cqqokjojk c iorf` mgmfjpvm pg fcab uctpoanf gi nokbp.Fojqpfoj qco` pbcp "capvcnn qbg{f` pbcp. vqojk Uncjahq tc`ocpogj nc{/ fcab ubgpgj
mvqp bcyf c iorf` cmgvjp gi fjftk. pbf fjftk svcjpvm = b. pbf dgn` jf{ o`fc
pbcp bc` lvqp dffj utgugqf` d Uncjah oj 3?55 "pbf igvj`cpogj gi svcjpvm ubqoaq.
cq lvqp `oqavqqf`/* [f {onn vqf F = bi. ojqpfc` gi pbf Ktffh qmdgnq* Bftf b oq pbf
Uncjah agjqpcjp cj` i oq pbf itfsvfja "gi pbf nokbp {cyf#/* Fojqpfoj {cq capvcnn
qcojk pbcp nokbp bcq `vcn jcpvtf. op oq dgpb c {cyf cj` cnqg c uctpoanf#
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qvticaf cj` hjgah gvp fnfaptgjq itgm {opboj pbf mfpcn* Pbf fnfaptgj {boab cuufctq
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pbf dcqoq gi pbf {cyf o`fc gi nokbp*
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7/31/2019 The Air Tran Story: The Merger and Maximum Point on Profits-Revenues Graph
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Uckf 15 gi05
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