copy Hun Myoung Park (542016) Midterm Exam 1

httpwwwsonsooorg

INTERNATIONAL UNIVERSITY OF JAPAN Public Management and Policy Analysis Program

Graduate School of International Relations

DCC5350 (2 Credits) Public Policy Modeling

Spring 2016

Midterm Exam (100 points) Instruction Please write down your student ID and name at the top of your answer You MUST always show necessary computation and your reasoning as clearly as possible When handling rational numbers (eg 31415) use at least three digits below the decimal point Question 1 (20 points) Suppose your goal is to get A from this Public Policy Modeling at IUJ in 2016 11 (5 points) Classify this problem in terms of level of knowledge staticdynamic and

strategicnonstrategic 12 (5 points) Identify at least three decision variables Specify the unit of measurement 13 (5 points) Identify at least three important environment variables Do not say for

example Obamarsquos preference (favorableunfavorable) for immigration policy that is rarely related to your getting A Specify the unit of measurement

14 (5 points) Identify at least three criterion variables Specify the unit of measurement

Thumb Up ()

Thumb Down ()

108

Stocks

50Growth (450)

-20Recess ()

-50Depress ()

5Growth (450)

10Recess ()

20Depress ()

Bonds

-222

Stocks

50Growth (033)

-20Recess (817)

-50Depress (150)

113

5Growth (033)

10Recess (817)

20Depress (150)

Bonds

Question 2 (30 points) Read Question 927 on page 375 and look at the decision tree under imperfect (sample) information above Some payoffs were changed and prior probabilities are P(Growth)=2 P(Recession)=7 and P(Depression)=1 Economy guru will thumb up or down to indicate his forecast and conditional probabilities are P(Up|Growth)=9 P(Up|Recession)=3 and P(Up|Depression)=1 21 (3 points) Construct a decision table (payoff table) with prior probabilities incorporated

copy Hun Myoung Park (542016) Midterm Exam 2

httpwwwsonsooorg

22 (3 points) Make a decision using EMV 23 (3 points) Construct the regret table 24 (3 points) Make a decision using EOL 25 (4 points) Calculate the expected value of perfect information Draw a decision tree

under perfect information 26 (7 points) Fill the blanks of and in the decision tree above 27 (4 points) Fill the blanks of and in the decision tree above 28 (3 points) If the guru asks 1 (price) for his forecasting would you like to buy it Why Question 3 (30 points) Look at Q58 on page 184 31 (5 points) Report the optimal solution and optimal value (of the objective function)

Show your calculation 32 (5 points) Interpret the meaning of the allowable increase and decrease of the third

coefficient You need to mention at least optimal solution and optimal value 33 (5 points) Interpret the meaning of a non-zero reduced cost substantively 34 (5 points) Fill the first (Final Value) and third (Constraint RHSide) blanks of constraint

1 (Milk) in the second part of the Excel output Show your calculation andor reasoning Ignore allowable increase and decrease

35 (5 points) Report slacksurplus of constraint 1 Show your calculation Is it slack or surplus What is the shadow price of constraint1 How did you know that

36 (5 points) Explain the meaning of the largest shadow price substantively Donrsquot forget to add the allowable range in your explanation

Question 4 (20 points) Remember the group project 1 Here you may use your grouprsquos answer or your own answer (if you donrsquot agree on the group answer) The following is the sensitivity report of Q27 Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$15 x1 12 0 33 1E+30 215

$C$15 x2 4 0 23 43 155

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price RH Side Increase Decrease

$B$17 Constraitn 1 x1 4 0 3 1 1E+30

$B$18 Constraitn 2 x1 44 0 18 26 1E+30

$B$19 Constraitn 3 x1 4 -0716666667 4 36 6

$B$20 x1 20 2583333333 20 1E+30 6

41 (3 points) Show how 23 under Objective Coefficient was calculated 42 (5 points) Check the unit of measurement of the objective function and second constraint 43 (3 points) Explain why reduced costs above are all zero 44 (5 points) Given the information above (donrsquot try to run Excel Solver) what would you

suggest for constraint 3 to maximize the benefit You must mention what you want to change and its consequence (result)

45 (4 points) Among certainty divisibility proportionality additivity and homogeneity which assumption do you think is most problematic in this LP formulation And why

End of the midterm exam

---------

dYh amiG I strate9Ic

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C) 9~- rjJC~ -ser~ kgt~ rUT shy

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Rf 9fet (stO~515rowt~) - so -so ~ ~e0et (~tod(S J ~ ecelS1~~) )6 - (--10)- 30

~ e~re t- (~ftCl~ J peprUJfon) gt0 (~20) ~ 70

t~ret (Jad~ I gro gtAi1 ) ~ 50 - 5 1~ II (bOric) 5 R fltpoundH o ) ~ 0 10 = ()

( ( k ctd4 DertJs i vn) vgt - JJ) 0

J~) ~eu~f()n WJ iOL EOL i (f r1O( rrVh~) iij ) (recyef-)

[OLIc~(hS (02)(0) + (O]J(3CJ) f (01)(70)

- J~

rol borlQS (o2)l45) + (0middot1)(0) +(OJ)(C)z

=- 4

tOL bonds I pound01 5tDcJvS I

~ DO lt ~S rshy

5UI ln veJ f n bondS teemiddot Jr pro if des IDwer (1 SF ~----

~ti1Q II er reg re r middot

IBS02Y LOUIE

EfftffecJ lIfo (02)[50) J- (0 t)[o) r(O)(~raquo)pound = ~-tt ~~--~----~-~--- ---------~------------

EV rt ~ euro~ pe rfeUt I~f) - (poundAll V

- fy - 0

qfvPI=shy j

(W3 r+ ihctl CVS~ poundeurotj(Y)J NJIS

1jqLve IS uf rNort-hrr1)hL e 10

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)e~(e)son 1)

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(b) 0middot1

CR)Ol 1c1 cole0ilie IlII 1A1I ~lilere~

feD) = omiddot rr( 1)jw Yl )~ GmiddotI

1gt (UP )b ) omiddot 9

( Do wtl 1 ~) = 0 1fcur R) ~ Gmiddot ) P(p 0 wh D ) omiddot q

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yrclctJl ~ D 0middot01omiddot ~ ~ 09

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(=p (Up 16) t ((Op IJ 1) + r(Up f p) 0IBJ OJHO() I

1t~ ~(UfJ) - 0middot4 i FtYl ~ f~w)Jt~ ~) =+hftl - f(t)wri) o~o ( b~ GOled1~e ~hqv~ h~()eJJ J fJ(Up H- p(Jdwn)1

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0 I- (9 qo)(oo) + O-~qr~--

If $3~J (5 v

3-d) 1he l)h]t profW ( bcmcm ~ ex)) CCir)

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~ory [ 120 I IGIDJ Meoni n9 if ihefl is iluea~e in le S)9q r res 0 ) ICe

hili IS6 10 ICoo I the Irol1 ltNJ1 iOCflaSe ~ $18 0- 1115 XIOJ

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2 I Jrtgt bvh i IitY

copy Hun Myoung Park (542016) Midterm Exam 2

httpwwwsonsooorg

22 (3 points) Make a decision using EMV 23 (3 points) Construct the regret table 24 (3 points) Make a decision using EOL 25 (4 points) Calculate the expected value of perfect information Draw a decision tree

under perfect information 26 (7 points) Fill the blanks of and in the decision tree above 27 (4 points) Fill the blanks of and in the decision tree above 28 (3 points) If the guru asks 1 (price) for his forecasting would you like to buy it Why Question 3 (30 points) Look at Q58 on page 184 31 (5 points) Report the optimal solution and optimal value (of the objective function)

Show your calculation 32 (5 points) Interpret the meaning of the allowable increase and decrease of the third

coefficient You need to mention at least optimal solution and optimal value 33 (5 points) Interpret the meaning of a non-zero reduced cost substantively 34 (5 points) Fill the first (Final Value) and third (Constraint RHSide) blanks of constraint

1 (Milk) in the second part of the Excel output Show your calculation andor reasoning Ignore allowable increase and decrease

35 (5 points) Report slacksurplus of constraint 1 Show your calculation Is it slack or surplus What is the shadow price of constraint1 How did you know that

36 (5 points) Explain the meaning of the largest shadow price substantively Donrsquot forget to add the allowable range in your explanation

Question 4 (20 points) Remember the group project 1 Here you may use your grouprsquos answer or your own answer (if you donrsquot agree on the group answer) The following is the sensitivity report of Q27 Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$15 x1 12 0 33 1E+30 215

$C$15 x2 4 0 23 43 155

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price RH Side Increase Decrease

$B$17 Constraitn 1 x1 4 0 3 1 1E+30

$B$18 Constraitn 2 x1 44 0 18 26 1E+30

$B$19 Constraitn 3 x1 4 -0716666667 4 36 6

$B$20 x1 20 2583333333 20 1E+30 6

41 (3 points) Show how 23 under Objective Coefficient was calculated 42 (5 points) Check the unit of measurement of the objective function and second constraint 43 (3 points) Explain why reduced costs above are all zero 44 (5 points) Given the information above (donrsquot try to run Excel Solver) what would you

suggest for constraint 3 to maximize the benefit You must mention what you want to change and its consequence (result)

45 (4 points) Among certainty divisibility proportionality additivity and homogeneity which assumption do you think is most problematic in this LP formulation And why

End of the midterm exam

---------

dYh amiG I strate9Ic

~BS-02q LOU1E

Ql Imiddot J Vlcertofl) 12 u) ah16 u~t 0 stvd~ 1i me ~rSI

b) score tf) HW I proj ects 1 rnfdJeryY)

C) atteurohdah~ Jn cl aSS V 13 fA) no or hooks QilCbe in lhe librar9 for borrQwifl9 urit~FJ

b) available time fOT consultatiot) fJ Til Dr Por~ J hrs shy

C) 9~- rjJC~ -ser~ kgt~ rUT shy

~------------~--------Jmiddot4) q euroioW] resu 1+ be cJr

b -------------- ~~ovld3YO vp Pr1Ject cco re

tectAJ- q(g fr ~t AC hvJ----~----Sror t

(cJJ~ ((JLvv ILC~hj1Vo~ CC~i-pound U lACPJCJk(f 0

u

--

Q~

JI Fb~off TeM (ifl of reTurn d iOieJJment )

-f State of Nato Ie - I~fAIter ntl Dep (e~s01Growth ReceSSion

--50

lnve~t in )jocKs -~O-~O- - ----shy

j

101n~)t i~ Bonds ~ -01 0)~rObabl itu omiddot~

~frior J

~-----~-

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10 gt -Cf 00

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re1v(~~ of- it) ve~tm amprt

dJ) Re3(et Table

Nahw~4 ~ret 6ro~ ~eCeS510f )ffredflO n

~lft(t)tnvt

1(1 ve1 til) ~toU( 0 3D 70

45 0 0irvves1 I~ eo~ 01 omiddot prior fmbubli ~ Omiddotl

Rf 9fet (stO~515rowt~) - so -so ~ ~e0et (~tod(S J ~ ecelS1~~) )6 - (--10)- 30

~ e~re t- (~ftCl~ J peprUJfon) gt0 (~20) ~ 70

t~ret (Jad~ I gro gtAi1 ) ~ 50 - 5 1~ II (bOric) 5 R fltpoundH o ) ~ 0 10 = ()

( ( k ctd4 DertJs i vn) vgt - JJ) 0

J~) ~eu~f()n WJ iOL EOL i (f r1O( rrVh~) iij ) (recyef-)

[OLIc~(hS (02)(0) + (O]J(3CJ) f (01)(70)

- J~

rol borlQS (o2)l45) + (0middot1)(0) +(OJ)(C)z

=- 4

tOL bonds I pound01 5tDcJvS I

~ DO lt ~S rshy

5UI ln veJ f n bondS teemiddot Jr pro if des IDwer (1 SF ~----

~ti1Q II er reg re r middot

IBS02Y LOUIE

EfftffecJ lIfo (02)[50) J- (0 t)[o) r(O)(~raquo)pound = ~-tt ~~--~----~-~--- ---------~------------

EV rt ~ euro~ pe rfeUt I~f) - (poundAll V

- fy - 0

qfvPI=shy j

(W3 r+ ihctl CVS~ poundeurotj(Y)J NJIS

1jqLve IS uf rNort-hrr1)hL e 10

~g

t

)SOlq OUE L~i brO vJh b --~---- Reces)P1 - R

)e~(e)son 1)

gVen

(b) 0middot1

CR)Ol 1c1 cole0ilie IlII 1A1I ~lilere~

feD) = omiddot rr( 1)jw Yl )~ GmiddotI

1gt (UP )b ) omiddot 9

( Do wtl 1 ~) = 0 1fcur R) ~ Gmiddot ) P(p 0 wh D ) omiddot q

( uP D ) omiddot 1

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P - (UP 1q P( O~ ~ 02 OmiddotI~

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(=p (Up 16) t ((Op IJ 1) + r(Up f p) 0IBJ OJHO() I

1t~ ~(UfJ) - 0middot4 i FtYl ~ f~w)Jt~ ~) =+hftl - f(t)wri) o~o ( b~ GOled1~e ~hqv~ h~()eJJ J fJ(Up H- p(Jdwn)1

P(J0 t4JY) J~ ff If) 1-04

1ftt ~ (Ol(r6~) t (o~l(ll3J __ J

p

tugtI t~It - t tl V

) CI EVSr II I - ID 00

J t~SI IJ

beG E~SI 11 )

Info 15 U()(01W~lLe to buc0 [et quru (~ advl~

Q3 ~(f2eJ-(L~)l~P

OpT f maL sor) s tu produce o

XJ 0 9a1On~ of c~oco J1e j~ creo IY]

Il~ IJ 30 II O~~ f vah J)q

~ b~C1hOX3 = 1)

fYJ(jX rroft 7lt + 0middot1Vh t ()~5)3

0 I- (9 qo)(oo) + O-~qr~--

If $3~J (5 v

3-d) 1he l)h]t profW ( bcmcm ~ ex)) CCir)

rClhge forn [OQO oq9J~] wID ofeGtJ~9I

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~ ~OO i5 -1lt tn(~i om cvrno()f ~ rY) It- CA J ~Oabe to f~Vl ~

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d jS Jb 1lt beG j IIVO lve5 the s~n ~ L C jf

1t MDltNns rJ 50 IQ MI) 1lt ole ndv vn1it-I amp

c)v~w Prt CQ ~ mll a nan bif) df)Q ConStrOv1igtto gt be c it is J

j ~ I The SnodolAl f riCSl of ~1S fur Sv90r is j+Q amount JhtAt

will be added I sohtdled 0 tlIe rna~ ifl1)~d profit ~r eve~ 1 gollon

~~(fea5euro f deueaSe in fhe OlQlabe sv3ar 1hJpound pncelt valid

~ory [ 120 I IGIDJ Meoni n9 if ihefl is iluea~e in le S)9q r res 0 ) ICe

hili IS6 10 ICoo I the Irol1 ltNJ1 iOCflaSe ~ $18 0- 1115 XIOJ

~middotI 1 ~1rA) pfbB ~ --roml GOs8 [OsSR t SLD t O2PD) - (IV t-2FM)

~5 ( OTV + IPIYl) 1-15( 3TV t 2Prfll t O~~1V t ~ Phl) - [ 11W- ~f MJ

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2 I Jrtgt bvh i IitY

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Ql Imiddot J Vlcertofl) 12 u) ah16 u~t 0 stvd~ 1i me ~rSI

b) score tf) HW I proj ects 1 rnfdJeryY)

C) atteurohdah~ Jn cl aSS V 13 fA) no or hooks QilCbe in lhe librar9 for borrQwifl9 urit~FJ

b) available time fOT consultatiot) fJ Til Dr Por~ J hrs shy

C) 9~- rjJC~ -ser~ kgt~ rUT shy

~------------~--------Jmiddot4) q euroioW] resu 1+ be cJr

b -------------- ~~ovld3YO vp Pr1Ject cco re

tectAJ- q(g fr ~t AC hvJ----~----Sror t

(cJJ~ ((JLvv ILC~hj1Vo~ CC~i-pound U lACPJCJk(f 0

u

--

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lnve~t in )jocKs -~O-~O- - ----shy

j

101n~)t i~ Bonds ~ -01 0)~rObabl itu omiddot~

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~-----~-

I

J) DeCiampl(jY1 wI EM

EMJ ~ g(ft1Of rrvbobli~)( poPffl

EMV ~wd~ (0middot 2) 50 ) t (OT)( - dO) + (01 )(-50)

~~OO

~ -

10 J

EM V bol dS gt EM V )to ckS I

10 gt -Cf 00

~erefo(p I in Vpound(t ill ~o~5 ~ec it 9ivf b8Hushy

re1v(~~ of- it) ve~tm amprt

dJ) Re3(et Table

Nahw~4 ~ret 6ro~ ~eCeS510f )ffredflO n

~lft(t)tnvt

1(1 ve1 til) ~toU( 0 3D 70

45 0 0irvves1 I~ eo~ 01 omiddot prior fmbubli ~ Omiddotl

Rf 9fet (stO~515rowt~) - so -so ~ ~e0et (~tod(S J ~ ecelS1~~) )6 - (--10)- 30

~ e~re t- (~ftCl~ J peprUJfon) gt0 (~20) ~ 70

t~ret (Jad~ I gro gtAi1 ) ~ 50 - 5 1~ II (bOric) 5 R fltpoundH o ) ~ 0 10 = ()

( ( k ctd4 DertJs i vn) vgt - JJ) 0

J~) ~eu~f()n WJ iOL EOL i (f r1O( rrVh~) iij ) (recyef-)

[OLIc~(hS (02)(0) + (O]J(3CJ) f (01)(70)

- J~

rol borlQS (o2)l45) + (0middot1)(0) +(OJ)(C)z

=- 4

tOL bonds I pound01 5tDcJvS I

~ DO lt ~S rshy

5UI ln veJ f n bondS teemiddot Jr pro if des IDwer (1 SF ~----

~ti1Q II er reg re r middot

IBS02Y LOUIE

EfftffecJ lIfo (02)[50) J- (0 t)[o) r(O)(~raquo)pound = ~-tt ~~--~----~-~--- ---------~------------

EV rt ~ euro~ pe rfeUt I~f) - (poundAll V

- fy - 0

qfvPI=shy j

(W3 r+ ihctl CVS~ poundeurotj(Y)J NJIS

1jqLve IS uf rNort-hrr1)hL e 10

~g

t

)SOlq OUE L~i brO vJh b --~---- Reces)P1 - R

)e~(e)son 1)

gVen

(b) 0middot1

CR)Ol 1c1 cole0ilie IlII 1A1I ~lilere~

feD) = omiddot rr( 1)jw Yl )~ GmiddotI

1gt (UP )b ) omiddot 9

( Do wtl 1 ~) = 0 1fcur R) ~ Gmiddot ) P(p 0 wh D ) omiddot q

( uP D ) omiddot 1

~

P - (UP 1q P( O~ ~ 02 OmiddotI~

Ab) P J6 ( ) OJJ

-

(J) (UI

f(vf~) ~ p(ur)~(f(~)) 03 x 0middot1 -

omiddoto~HVf (l ) ) f ( Vf Iiraquo - rev) O I x Omiddot I

(PO IN n ( amp ) - 0middot1 1 omiddot 2- Omiddot 0(p(PGwrgt () ~raquo 0 1 f 0middot1 - Omiddot~q (o~ A-JeJLL P(J70WI (lD) ~ 09 Ilt (71 ~ o-O~) rkj c~v

yrclctJl ~ D 0middot01omiddot ~ ~ 09

0-0 1

i IuJo J

BSOL9 ~

~ P ( D Up ) gt

~~trJ(Iond5 Vp) = (o4~QllS_ (O~2S-)( J6) t( OmiddotO~5)(~O) ~ g4

(=p (Up 16) t ((Op IJ 1) + r(Up f p) 0IBJ OJHO() I

1t~ ~(UfJ) - 0middot4 i FtYl ~ f~w)Jt~ ~) =+hftl - f(t)wri) o~o ( b~ GOled1~e ~hqv~ h~()eJJ J fJ(Up H- p(Jdwn)1

P(J0 t4JY) J~ ff If) 1-04

1ftt ~ (Ol(r6~) t (o~l(ll3J __ J

p

tugtI t~It - t tl V

) CI EVSr II I - ID 00

J t~SI IJ

beG E~SI 11 )

Info 15 U()(01W~lLe to buc0 [et quru (~ advl~

Q3 ~(f2eJ-(L~)l~P

OpT f maL sor) s tu produce o

XJ 0 9a1On~ of c~oco J1e j~ creo IY]

Il~ IJ 30 II O~~ f vah J)q

~ b~C1hOX3 = 1)

fYJ(jX rroft 7lt + 0middot1Vh t ()~5)3

0 I- (9 qo)(oo) + O-~qr~--

If $3~J (5 v

3-d) 1he l)h]t profW ( bcmcm ~ ex)) CCir)

rClhge forn [OQO oq9J~] wID ofeGtJ~9I

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wnci x 3 - 15 Bu I dh to l) lt 0 tht voiVll

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d jS Jb 1lt beG j IIVO lve5 the s~n ~ L C jf

1t MDltNns rJ 50 IQ MI) 1lt ole ndv vn1it-I amp

c)v~w Prt CQ ~ mll a nan bif) df)Q ConStrOv1igtto gt be c it is J

j ~ I The SnodolAl f riCSl of ~1S fur Sv90r is j+Q amount JhtAt

will be added I sohtdled 0 tlIe rna~ ifl1)~d profit ~r eve~ 1 gollon

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~ory [ 120 I IGIDJ Meoni n9 if ihefl is iluea~e in le S)9q r res 0 ) ICe

hili IS6 10 ICoo I the Irol1 ltNJ1 iOCflaSe ~ $18 0- 1115 XIOJ

~middotI 1 ~1rA) pfbB ~ --roml GOs8 [OsSR t SLD t O2PD) - (IV t-2FM)

~5 ( OTV + IPIYl) 1-15( 3TV t 2Prfll t O~~1V t ~ Phl) - [ 11W- ~f MJ

O5PM t ~S1V t 3P~ - aLTV t (~PM -11 -~ J J

- 35 11 + 2s FM --

2) Con~tco int 2 1 J~J 3 TV

CJ ~) (1 WJ t (2 ~)(1 fgtgt1) ~ 9 o~

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2 I Jrtgt bvh i IitY

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j

101n~)t i~ Bonds ~ -01 0)~rObabl itu omiddot~

~frior J

~-----~-

I

J) DeCiampl(jY1 wI EM

EMJ ~ g(ft1Of rrvbobli~)( poPffl

EMV ~wd~ (0middot 2) 50 ) t (OT)( - dO) + (01 )(-50)

~~OO

~ -

10 J

EM V bol dS gt EM V )to ckS I

10 gt -Cf 00

~erefo(p I in Vpound(t ill ~o~5 ~ec it 9ivf b8Hushy

re1v(~~ of- it) ve~tm amprt

dJ) Re3(et Table

Nahw~4 ~ret 6ro~ ~eCeS510f )ffredflO n

~lft(t)tnvt

1(1 ve1 til) ~toU( 0 3D 70

45 0 0irvves1 I~ eo~ 01 omiddot prior fmbubli ~ Omiddotl

Rf 9fet (stO~515rowt~) - so -so ~ ~e0et (~tod(S J ~ ecelS1~~) )6 - (--10)- 30

~ e~re t- (~ftCl~ J peprUJfon) gt0 (~20) ~ 70

t~ret (Jad~ I gro gtAi1 ) ~ 50 - 5 1~ II (bOric) 5 R fltpoundH o ) ~ 0 10 = ()

( ( k ctd4 DertJs i vn) vgt - JJ) 0

J~) ~eu~f()n WJ iOL EOL i (f r1O( rrVh~) iij ) (recyef-)

[OLIc~(hS (02)(0) + (O]J(3CJ) f (01)(70)

- J~

rol borlQS (o2)l45) + (0middot1)(0) +(OJ)(C)z

=- 4

tOL bonds I pound01 5tDcJvS I

~ DO lt ~S rshy

5UI ln veJ f n bondS teemiddot Jr pro if des IDwer (1 SF ~----

~ti1Q II er reg re r middot

IBS02Y LOUIE

EfftffecJ lIfo (02)[50) J- (0 t)[o) r(O)(~raquo)pound = ~-tt ~~--~----~-~--- ---------~------------

EV rt ~ euro~ pe rfeUt I~f) - (poundAll V

- fy - 0

qfvPI=shy j

(W3 r+ ihctl CVS~ poundeurotj(Y)J NJIS

1jqLve IS uf rNort-hrr1)hL e 10

~g

t

)SOlq OUE L~i brO vJh b --~---- Reces)P1 - R

)e~(e)son 1)

gVen

(b) 0middot1

CR)Ol 1c1 cole0ilie IlII 1A1I ~lilere~

feD) = omiddot rr( 1)jw Yl )~ GmiddotI

1gt (UP )b ) omiddot 9

( Do wtl 1 ~) = 0 1fcur R) ~ Gmiddot ) P(p 0 wh D ) omiddot q

( uP D ) omiddot 1

~

P - (UP 1q P( O~ ~ 02 OmiddotI~

Ab) P J6 ( ) OJJ

-

(J) (UI

f(vf~) ~ p(ur)~(f(~)) 03 x 0middot1 -

omiddoto~HVf (l ) ) f ( Vf Iiraquo - rev) O I x Omiddot I

(PO IN n ( amp ) - 0middot1 1 omiddot 2- Omiddot 0(p(PGwrgt () ~raquo 0 1 f 0middot1 - Omiddot~q (o~ A-JeJLL P(J70WI (lD) ~ 09 Ilt (71 ~ o-O~) rkj c~v

yrclctJl ~ D 0middot01omiddot ~ ~ 09

0-0 1

i IuJo J

BSOL9 ~

~ P ( D Up ) gt

~~trJ(Iond5 Vp) = (o4~QllS_ (O~2S-)( J6) t( OmiddotO~5)(~O) ~ g4

(=p (Up 16) t ((Op IJ 1) + r(Up f p) 0IBJ OJHO() I

1t~ ~(UfJ) - 0middot4 i FtYl ~ f~w)Jt~ ~) =+hftl - f(t)wri) o~o ( b~ GOled1~e ~hqv~ h~()eJJ J fJ(Up H- p(Jdwn)1

P(J0 t4JY) J~ ff If) 1-04

1ftt ~ (Ol(r6~) t (o~l(ll3J __ J

p

tugtI t~It - t tl V

) CI EVSr II I - ID 00

J t~SI IJ

beG E~SI 11 )

Info 15 U()(01W~lLe to buc0 [et quru (~ advl~

Q3 ~(f2eJ-(L~)l~P

OpT f maL sor) s tu produce o

XJ 0 9a1On~ of c~oco J1e j~ creo IY]

Il~ IJ 30 II O~~ f vah J)q

~ b~C1hOX3 = 1)

fYJ(jX rroft 7lt + 0middot1Vh t ()~5)3

0 I- (9 qo)(oo) + O-~qr~--

If $3~J (5 v

3-d) 1he l)h]t profW ( bcmcm ~ ex)) CCir)

rClhge forn [OQO oq9J~] wID ofeGtJ~9I

-rre opjmCil L So vtlO ns of I lt 0 ) 11 ~ 3(

wnci x 3 - 15 Bu I dh to l) lt 0 tht voiVll

Of +k ~ rohf l-1JJI C~Cx 0 u

lO lI te ) B )flJ

----_ I 1 ~

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d jS Jb 1lt beG j IIVO lve5 the s~n ~ L C jf

1t MDltNns rJ 50 IQ MI) 1lt ole ndv vn1it-I amp

c)v~w Prt CQ ~ mll a nan bif) df)Q ConStrOv1igtto gt be c it is J

j ~ I The SnodolAl f riCSl of ~1S fur Sv90r is j+Q amount JhtAt

will be added I sohtdled 0 tlIe rna~ ifl1)~d profit ~r eve~ 1 gollon

~~(fea5euro f deueaSe in fhe OlQlabe sv3ar 1hJpound pncelt valid

~ory [ 120 I IGIDJ Meoni n9 if ihefl is iluea~e in le S)9q r res 0 ) ICe

hili IS6 10 ICoo I the Irol1 ltNJ1 iOCflaSe ~ $18 0- 1115 XIOJ

~middotI 1 ~1rA) pfbB ~ --roml GOs8 [OsSR t SLD t O2PD) - (IV t-2FM)

~5 ( OTV + IPIYl) 1-15( 3TV t 2Prfll t O~~1V t ~ Phl) - [ 11W- ~f MJ

O5PM t ~S1V t 3P~ - aLTV t (~PM -11 -~ J J

- 35 11 + 2s FM --

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CJ ~) (1 WJ t (2 ~)(1 fgtgt1) ~ 9 o~

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- The 1I~bev ()f ~lAes~o hS Cr~eJ It cfe-rr peK w~t-

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- C~e p6((i er doSChd Ik 1-4 7(fc~lt-o

- LD (115 0trvfe~ Jeov- ~J AlA f1(e~1( eJ VI skJ7 ifshy

L4 - ~~ I eo- rV e d itA J-~ Wi J t-e Y CUlJ ft~ ~~s

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- -S(ov-e I ENV-l J 1 9tA)

De(lt~ro2 G VlJwH Dept-eS~-dt

ltodes ~O -20 -50 3oJ middots 10 20

2 I Jrtgt bvh i IitY

dJ) Re3(et Table

Nahw~4 ~ret 6ro~ ~eCeS510f )ffredflO n

~lft(t)tnvt

1(1 ve1 til) ~toU( 0 3D 70

45 0 0irvves1 I~ eo~ 01 omiddot prior fmbubli ~ Omiddotl

Rf 9fet (stO~515rowt~) - so -so ~ ~e0et (~tod(S J ~ ecelS1~~) )6 - (--10)- 30

~ e~re t- (~ftCl~ J peprUJfon) gt0 (~20) ~ 70

t~ret (Jad~ I gro gtAi1 ) ~ 50 - 5 1~ II (bOric) 5 R fltpoundH o ) ~ 0 10 = ()

( ( k ctd4 DertJs i vn) vgt - JJ) 0

J~) ~eu~f()n WJ iOL EOL i (f r1O( rrVh~) iij ) (recyef-)

[OLIc~(hS (02)(0) + (O]J(3CJ) f (01)(70)

- J~

rol borlQS (o2)l45) + (0middot1)(0) +(OJ)(C)z

=- 4

tOL bonds I pound01 5tDcJvS I

~ DO lt ~S rshy

5UI ln veJ f n bondS teemiddot Jr pro if des IDwer (1 SF ~----

~ti1Q II er reg re r middot

IBS02Y LOUIE

EfftffecJ lIfo (02)[50) J- (0 t)[o) r(O)(~raquo)pound = ~-tt ~~--~----~-~--- ---------~------------

EV rt ~ euro~ pe rfeUt I~f) - (poundAll V

- fy - 0

qfvPI=shy j

(W3 r+ ihctl CVS~ poundeurotj(Y)J NJIS

1jqLve IS uf rNort-hrr1)hL e 10

~g

t

)SOlq OUE L~i brO vJh b --~---- Reces)P1 - R

)e~(e)son 1)

gVen

(b) 0middot1

CR)Ol 1c1 cole0ilie IlII 1A1I ~lilere~

feD) = omiddot rr( 1)jw Yl )~ GmiddotI

1gt (UP )b ) omiddot 9

( Do wtl 1 ~) = 0 1fcur R) ~ Gmiddot ) P(p 0 wh D ) omiddot q

( uP D ) omiddot 1

~

P - (UP 1q P( O~ ~ 02 OmiddotI~

Ab) P J6 ( ) OJJ

-

(J) (UI

f(vf~) ~ p(ur)~(f(~)) 03 x 0middot1 -

omiddoto~HVf (l ) ) f ( Vf Iiraquo - rev) O I x Omiddot I

(PO IN n ( amp ) - 0middot1 1 omiddot 2- Omiddot 0(p(PGwrgt () ~raquo 0 1 f 0middot1 - Omiddot~q (o~ A-JeJLL P(J70WI (lD) ~ 09 Ilt (71 ~ o-O~) rkj c~v

yrclctJl ~ D 0middot01omiddot ~ ~ 09

0-0 1

i IuJo J

BSOL9 ~

~ P ( D Up ) gt

~~trJ(Iond5 Vp) = (o4~QllS_ (O~2S-)( J6) t( OmiddotO~5)(~O) ~ g4

(=p (Up 16) t ((Op IJ 1) + r(Up f p) 0IBJ OJHO() I

1t~ ~(UfJ) - 0middot4 i FtYl ~ f~w)Jt~ ~) =+hftl - f(t)wri) o~o ( b~ GOled1~e ~hqv~ h~()eJJ J fJ(Up H- p(Jdwn)1

P(J0 t4JY) J~ ff If) 1-04

1ftt ~ (Ol(r6~) t (o~l(ll3J __ J

p

tugtI t~It - t tl V

) CI EVSr II I - ID 00

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Info 15 U()(01W~lLe to buc0 [et quru (~ advl~

Q3 ~(f2eJ-(L~)l~P

OpT f maL sor) s tu produce o

XJ 0 9a1On~ of c~oco J1e j~ creo IY]

Il~ IJ 30 II O~~ f vah J)q

~ b~C1hOX3 = 1)

fYJ(jX rroft 7lt + 0middot1Vh t ()~5)3

0 I- (9 qo)(oo) + O-~qr~--

If $3~J (5 v

3-d) 1he l)h]t profW ( bcmcm ~ ex)) CCir)

rClhge forn [OQO oq9J~] wID ofeGtJ~9I

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wnci x 3 - 15 Bu I dh to l) lt 0 tht voiVll

Of +k ~ rohf l-1JJI C~Cx 0 u

lO lI te ) B )flJ

----_ I 1 ~

100 YJ - tBro re 01 (A ad CO)J of33) 111e At C1 rntmiddot-0 O~15 +by A is

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