Optimization problem mourn'numinar

Bustos optimization MUseqnoiforiwomnhn innr.nuHis moiotumroofornstiniscierianoinafswolorfsogn

moaiohiuminwqoggdsnfwndoiouvsefrs.nu'gorio

Y a f xdy f'Cx do first derivativedI Cntslope

tow Y FCK 1004 2X

dy f x 2 slope IDX

guy y fCx 4 2 16 130

dy 8 16 slopede

n'gangsagaloiingn f Cx o slope o

8 16 0x e Critical valuemm

pinngsy Xo

mnnhfngoinnaogunwnhxnbwnoymngnhong.MN f'Cxbadoo.dz f x 70 Moto flex co

X il X 3ii XXo 2 v

F i 847 16 a g L O

3 F 3 a 8137 16 8 SO

Momo'sn'owotbqnon.gr Slope 20

n uTsqn8nyn slope o

Yfl r 820

f n sofC2 mg

xXo2

riuouqoiidutn.in

Y Y fCx

If'cx oto

1 xXo

maroon'ingsojn lotion Inomoan Second derivative

0in Y FCKdy file first derivative

dy f x first derivativedIday f Cx Second derivativeDT2

f Xo 70 normal Y fan Bunhriingn

Xo noo critical valuef Xo 20 uomo Y flea Bun'inorgn

roil is'oaduntradoomedingongnloingnoosntonrow

Necessary condition u8o First order conditionCFOcHomo F'Cx O unboanga Xo

Sufficient conditionnodo Second ordercondition CS0CIDoorman f exo inunhroisqnloiignJnu f Cx so n'notion

f Xo 20 n'inform

ooonvo1005 utilityU b X Xz Xn

ooonuretoowniownbnrwucs.BA i ran

U CX

Total utility TU Cooonusiloonison

nonarroionounaritotommsustanBwny

TU TUmay

YTTV

xXo Conrow

Marginal utility MU ooondoioowba.gr

do noiwwoondhotooanmoustanowniin.groh 7 seadog

MU dTUDX

law of diminishing MuDTowotnnBuminin n redder MU oeintarlisonsininoing

TU MU

th

iTom x

Hooda uCx zx 313

un

intone Tv q2

yz3

MU ACTU Sx 2

FXri TU agongn slopenos Tu 0 Ufo Mu O

MU a

SX x2 O

S K O

X O 5

n7 Second order condition

D8 dCsx K2 s 2x e Xdt2 DX

nu x O u a 5 So u oingo

s u s g lo S L O Unfoogn

awow8wnY Cx nn'Tailor utility foopino s MisterTU MU

TVmax Tumor TU S

If utiµ ages2yesss

i 125Xo I

a

mood production

TP Q f L k 7 msevdoioer.INQ errendon throw Komori

e TP Q f L info k roof

law of diminishing returns

ndmsanmioonoonsvogown.si

Average Product AP anodonanto

ErnodnottotoinmdEDotoetwins a unitAP AP a PL

L 3 Dotoarwicus

Marginal product Mp anadordouin'd

Oriordanintartwanmnterundomination a unit

Mp MP d TP fL Lde

TP Mp

gI

µ'T Tp

AP1

Mpe

nanntwaterforeo'D TP Nu Mpfestoon TP in'gfwetorrinental TPP Mppfestoon TP thighwoorandanas TPP MP I 11MMp o

goinTPnggqn rip 01240 TPd Mp Gnau

MtNGwaw8su APnmpfascism AP thin MP 2 AP

MP AP NF AP fornAPPhDs MPC AP

21 2 62

II Homework Wide

finding7 MP AP F'AP sn

Hint Q fa ko

AP the Mp dqrt AP forgo slopeuo.tt

oAPpL fCIL

slope AP deaf da f O

jd f d O

GIFs

idfaDT diff fat

erdfa fCLDL L

dCTP TpDL L

Mp AP

079004 Wgrirwmorowfm Q L t 4L 0.4L TPin

Montague's AP MP of APEggo

m AP IPL Oz LL

Ap I t 4L 0.412 L

imma FiMp

AP MPFAPq98or Apna slope AP O

m slopeAP DEAL 0dL DL

4 0.8L O

c ghmm

hmmri L s ginettaApmax

HAE AP MP

AP of L 5 Ap I t 4L 0.422

it 4cg 0.4125 11Mp GTi 5 Mp n t 8L 1.212

It 8157 1.2125 11

i L s AP Mp

By graphinnTPMP AP

gTP

i

nap

I Lg

Tpmax

r Foe DTP O baton Critical valueTd Lo

D Soc DIP LO Tpmaxdt2

Fcc If t 4L 0.4lb 0dL

ax't be 1C y t 8L 7.212 om

b THAT o

SIT64 447C1.27 0

O

L 6.78 072Wr

SEC dKTP7 20DT2

ad 748L 1.2L 8 2.4LL

knw L 6.78 8 2.4 6.78

8.27 L O

ond 6.78 TpmaxJocund Tpmax L t 4L 0.4L's

6.78 t 416.7872 0.416.7873

65.99 a 66

By graphinnTPMP APby sql TP

if me y

tmpPI e5 6.78

Nanwmsw5n cost

TC C C Q C costa output

oingwson Totalcost TC

TC TVC t TFC

Tvc Total variablecost oiwqwerw.no

TFC CTotal fixed cost ringwnortood

TC TVC T TFCEl or adoingwoodo Average cost Ac

oiwyweiuuvsoo.de Average variable cost AvaAVC TVC

I

oiwqunon.info C Average fixedcost Apc

AFC TFCI

misquotations Marginal cost MC

oiwywnintwoiwmnmsoforowoiii.si'w8n i unit

MC dCTCTQ

TC TFC t TVC

DEC DIFC t d Cda da da

MC O t d VC

TQ

MC d TVCdot

MC AC AVCAFC

1n

MC Ac F AC simianMC AVC T Aucoin'qn

Tvc JFCstood TC QTt5Qft

gsmseoiuanerdornn.TW MC AVC

op MC Auc Auc opinion

m MC an MC DTC 302GQ 115

DOT

H7 AVC 97N AVC Tvc Q 301 15QQ Q

Auc Q2 3Q 115

D atAucmin slopeoaninu 0

slopeAuc d Auc odot

IQ 3 C

Q 32

SO C badonnoradi G 3g nikita Aucoinno8gDYAK dC2Q 3 2 O minda2 da

nd Q 3g Auc Q 3Q 115 323C 115

22.75b MC 302 60 115

31372 BCE 115

12.75

in Q z n'Art MC Auc 1275