Q1.BoundsInc.hasdeterminedthrough regressionanalysisthatitssales(S)areafunction oftheamount of advertising (measured in units) in two different media. This is given by thefollowingrelationship (X=newspapers, Y=magazines):

S(X,Y)= 200X+100Y-10X2-20Y2+20XY

1. Findthelevelofnewspaperandmagazineadvertisingthatmaximizesthefirm'ssales.
2. Calculatethefirm'ssalesattheoptimallevelnewspaperandmagazineadvertisingdeterminedin part (A), and provethatthis sales levelis a maximum.
3. Nowassumethat theadvertising budgetis restrictedto20 units.
4. Determine thelevel of newspaper and magazine advertising that maximizessalessubjecttothisbudgetconstraintusingtheLagrangianmultipliertechnique.
5. Calculatethefirm'ssales atthisconstrainedoptimum level.
6. GiveaneconomicinterpretationofthevalueoftheLagrangianmultiplier - (l)obtained inpart (i).
7. Comparethe answer obtained in parts (i) and (ii) above with the optimalsolutionto the unconstrained problemin parts (A)and(B)above.

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Q2. The Palestinian Museum is a showroom for avant-garde artwork that is located in ZeitgeistCity.Thecuratorofthemuseum)(,Ikhlasisanartistwithakeenbusinesssense.In additiontoherownwork, shedisplaysarttakenonconsignmentandpiecesthatshepurchases on her annual business trips to Europe, where some Palestinian artists live in exile. She iscurrently considering the purchase of works by two Palestinian artists. One is a relativeunknown and the other is a mature artist of some stature. She must choose between the twoandwillbaseherdecisiononthefollowingassessmentoftheirpotentialvalue.AhmadRushdiis a vigorous young Palestinian artist noted for his anamorphic images of old kitchen tools.His set of six oil paintings can be purchased for $5,000 at the current exchange rate. Ikhlasfeels that the probability (P)distribution of potential profits ()from the purchase ofAhmad'spaintings (in $1,000s) inPalestine is as follows:

p	-4	1	3	5
P	0.2	0.4	0.3	0.1

KifahSuleimanisaPalestinianwhohasestablishedareputationasamaster ofdrollery(

).Sheoffersaset ofsignedandnumberedvelvetpaintingsentitled""for$10,000. While Ikhlaswould not ordinarily be interested in this type of art, she has heard rumors thatKifah'sfreneticlifestyleistakingitstollonherhealth andthat,astheysay,itisonlyamatterof time. If Kifah dies, her work may increase substantially in value. Ikhlasbelieves that theprobabilitydistribution ofpotential profits (in $1,000s) fromKifah'sprints is as follows:

p	-2	4	32
P	0.6	0.35	0.05

Usethisinformationtosolvethefollowing:

1. Calculatetheexpectedprofitforeachoftheartworks.Whichshouldbeselected onthebasisof theexpected valuecriterion?
2. Calculatethestandarddeviation ofprofitforeachoftheartworks.Whichistheriskierof the two?
3. Usethecoefficient of variationtodeterminewhichof thetwo artworksispreferable.
4. Ikhlashasestimatedthatherutility ofprofitfunction(whereprofitsaremeasuredin

$1,000s)is

U= 20 -0.12

Usethisutilityfunction tocalculatetheexpectedutility ofeachoftheartworks.Whichofthetwo does Ikhlas prefer?Is shea risk seeker,arisk averter, orrisk-neutral?

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Q4. The Costa Coffee Company (For short Costa) is anticipating a major expansion of itsfranchisedcoffeeoutlets intoEuropeandAfricancountries.Theinvestmentopportunitiesavailabletothecompanyinvolve ratesofreturn andinitialinvestmentamountsthatdifferbecauseof differences in operating costs and consumer demand in the countries involved. The totalinvestment (K) that Costa can undertake is constrained by the cost of capital (i), which is definedbythe followingfunction:

i = 6 + 0.8 K

Theinitialinvestmentandrateofreturnforeachcountryarelistedbelowinorderofdecreasingrate ofreturn.

Country	InitialInvestment($ millions)	Rateof Return(%)
SouthAfrica	3.8	16.0
Kenya	1.3	15.0
France	2.4	13.0
Germany	3.1	11.0
Ethiopia	1.9	9.0

1. Plottheinvestmentsupplyfunctionandtheinvestmentdemandscheduleonthegraphbelow.
2. Determinetheoptimallevelofinvestmentandthecorrespondingcostofcapitalforthefirm.

18 16 Rate of Return(i) A O 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Capital Investment (K)\f18 16 14 12 10 8 ONA 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14