Name: Le Duc Thinh ID: BABAIU14255 QUANTITATIVE METHODS FOR BUSINESS -------------------------------------------------------------------------------------ASSIGNMENT ASSIGNMEN T: DECISION ANALYSIS ANALYSIS 3-19: The The Lubr Lubric ican antt is an expe expens nsiv ive e oil oil nes nesle lette tterr to hic hich h man! man! oil oil "ian "iants ts
subscribe# inclu$in" %en Bron &see 'roblem ()1* +or $etails,- In the last issue# the lett letter er $esc $escrib ribe$ e$ ho ho the the $ema $eman$ n$ +or +or oil oil pro$ pro$uc ucts ts oul oul$ $ be extr extrem emel! el! hi"h hi"h- Apparentl!# Apparentl!# the American consumer consumer ill continue to use oil pro$ucts even i+ the price o+ these pro$ucts $oubles- In$ee$# one o+ the articles in the Lubricant states that the chances o+ a +avorable mar.et +or oil pro$ucts as */0# hile the chance o+ an un+avorable mar.et as onl! (/0- %en oul$ li.e to use these probabilities in $eterminin" the best $ecision&a, hat $ecision mo$el shoul$ be use$ &b, hat is the optimal $ecision &c, %en believes that the 3(//#/// +i"ure +or the ub 1// ith a +avorable mar.et is too hi"h- o much loer oul$ this +i"ure have to be +or %en to chan"e his $ecision ma$e in part &b, 67UI'86NT ub 1// ;iler = Texan
9A;
UN9A;2//#/// >1//#/// >1?#///
olution: &a, Because this is a $ecision ma.in" hen there are several possible states o+ nature an$ e .no the probabilities associate$ ith each possible state@ there+ore# e ill use the 8aximie 6xpecte$ 8onetar! alue &68, mo$el in hich e choose the alternative ith the hi"hest 68&b, e have: 68&ub 1//, &/-*,C&3(//#///, &/-(,C&>32//#///, 315/#/// 68&;iler =, &/-*,C&325/#///, &/-(,C&>31//#///, 3145#/// 68&Texan, &/-*,C&3*5#///, &/-(,C&>31?#///, 34*#1// Depen$in" on the 8aximie 6xpecte$ 8onetar! alue mo$el# %ent shoul$ purchase a ub 1//# hich has the hi"hest 68&c, %en shoul$ chan"e his $ecision hen ub 1//Es 68 be eFual to the next best one# ;iler =- Let G be the +i"ure +or the ub 1// ith a +avorable mar.et# e have: 68&ub 1//, 3145#/// &/-*,CG &/-(,C&>32//#///, &/-*,CG > 3H/#///
G
≈
322#?5*-14( &or 3*142-?5* loer,
ence# the +i"ure +or the ub 1// ith a +avorable mar.et have to be 3*142-?5* loer +or %en to chan"e his $ecision-
Name: Le Duc Thinh ID: BABAIU14255
3-20: 8ic.e! Lason is consi$erin" investin" some mone! that he inherite$- The
+olloin" pa!o++ table "ives the pro+its that oul$ be realie$ $urin" the next !ear +or each o+ three investment alternatives 8ic.e! is consi$erin": &a, hat $ecision oul$ maximie expecte$ pro+its &b, hat is the maximum amount that shoul$ be pai$ +or a per+ect +orecast o+ the econom! D6JII;N ALT6
TAT6 ;9 NATU<6 K;;D 6J;N;8
toc. mar.et Bon$s JDs 'robabilit!
80,000
(/#/// 2(#/// /-5
';;< 6J;N;8 >2/#/// 2/#/// 23,000
/-5
olution: &a, Usin" the possible pro+its an$ probabilities in the table# e have the expecte$ pro+its +or each $ecision are as +ollos: 68&toc. mar.et, &/-5,C&3?/#///, &/-5,C&>32/#///, 3(/#/// 68&Bon$s, &/-5,C&3(/#///, &/-5,C&32/#///, 325#/// 68&JDs, &/-5,C&32(#///, &/-5,C&32(#///, 32(#/// Depen$in" on the 8aximie 6xpecte$ 8onetar! alue mo$el# 8ic.e! Lason shoul$ invest in stoc. mar.et# hich has the hi"hest 68# to maximie expecte$ pro+it&b, Best alternative +or +avorable an$ un+avorable state o+ nature is invest in stoc. mar.et ith a pa!o++ o+ 3?/#/// an$ invest in JDs ith a pa!o++ o+ 32(#///# respectivel!- e have: 6&ith pre+ect in+ormation, &/-5,C&3?/#///, &/-5,C&32(#///, 351#5// 6'I 6&ith pre+ect in+ormation, > 8aximum 68&ithout pre+ect in+ormation, 351#5// > 3(/#/// 321#5// o# the maximum 8ic.e! Lason shoul$ pa! +or a per+ect +orecast o+ the econom! is 321#5//-
3-21: Develop an opportunit! loss table +or the investment problem that 8ic.e!
Lason +aces in 'roblem ()2/- hat $ecision oul$ minimie the expecte$ opportunit! loss hat is the minimum 6;L olution:
Name: Le Duc Thinh ID: BABAIU14255 Best alternative +or +avorable an$ un+avorable state o+ nature is invest in stoc. mar.et ith a pa!o++ o+ 3?/#/// an$ invest in JDs ith a pa!o++ o+ 32(#///@ respectivel!e have the opportunit! loss table +or the investment problem that 8ic.e! Lason +aces as +olloin": D6JII;N ALT6
TAT6 ;9 NATU<6 K;;D ';;< 6J;N;8 6J;N;8 ?/#/// > ?/#/// / 2(#/// > &>2/#///, ?/#/// > (/#/// 4(#/// 5/#/// 2(#/// > 2/#/// ?/#/// > 2(#/// (#/// 5*#/// 2(#/// > 2(#/// / /-5 /-5
8AGI8U8 IN A <; &3, 43,000
5/#/// 5*#/// >
Depen$in" on the table# e can see that investin" in stoc. mar.et has the loest opportunit! loss@ there+ore# 8ic.e! Lason shoul$ invest in stoc. mar.et to minimie the expecte$ opportunit! losse have: 6;L&toc. mar.et, &/-5/,&3/, &/-5/,&34(#///, 321#5// 6;L&Bon$s, &/-5/,&35/#///, &/-5/,&3(#///, 32H#5// 6;L&JDs, &/-5/,&35*#///, &/-5/,&3/, 32?#5// o# the minimum 6;L ill happen hen 8ic.e! invests in stoc. mar.et# hich eFuals 321#5//-
Name: Le Duc Thinh ID: BABAIU14255 3-24:
To$a!Es 6lectronics
specialies
in
manu+acturin"
mo$ern
electronic
components- It also buil$s the eFuipment that pro$uces the components- 'h!llis einber"er# ho is responsible +or a$visin" the presi$ent o+ To$a!Es 6lectronics on electronic manu+acturin" eFuipment# has $evelope$ the +olloin" table concernin" a propose$ +acilit!: &a, Develop an opportunit! loss table&b, hat is the minimax re"ret $ecision
Lar"e +acilit! 8e$ium)sie$ +acilit! mall +acilit! No +acilit!
T<;NK 8A<%6T
'<;9IT &3, 9AI< 8A<%6T
';;< 8A<%6T
55/#/// (//#/// 2//#/// /
11/#/// 12#/// 1//#/// /
>(1/#/// >1//#/// >(2#/// /
olution: &a, Best alternative +or stron"# +air an$ poor mar.et is havin" lar"e +acilit! ith a pa!o++ o+ 355/#///@ me$ium)sie$ +acilit! ith a pa!o++ o+ 312#/// an$ no +acilit! ith a pa!o++ o+ 3/# respectivel!- e have the opportunit! loss table as +olloin":
Lar"e +acilit! 8e$ium) sie$ +acilit! mall +acilit!
No +acilit!
T<;NK 8A<%6T 55/#/// > 55/#/// / 55/#/// > (//#/// 25/#///
'<;9IT &3, 9AI< 8A<%6T 12#/// > 11/#/// 1#/// 12#/// > 12#/// /
55/#/// > 2//#/// (5/#///
12#/// > 1//#/// 2#///
55/#/// > / 55/#///
12#/// > / 12#///
';;< 8A<%6T / > &> (1/#///, (1/#/// / > &> 1//#///, 1//#///
8AGI8U8 IN A <; &3, (1/#/// 20,000
(5/#/// / > &>(2#///, (2#/// 55/#/// />/ /
&b, Depen$in" on the table# e can see that havin" me$ium)sie$ +acilit! has the loest opportunit! loss@ there+ore# To$a!Es 6lectronics shoul$ have me$ium)sie$ +acilit!-
Name: Le Duc Thinh ID: BABAIU14255
3-2: Brilliant Jolor is a small supplier o+ chemicals an$ eFuipment that are use$ b!
some photo"raphic stores to process (5mm +ilm- ;ne pro$uct that Brilliant Jolor supplies is BJ)H- =ohn %ubic.# presi$ent o+ Brilliant Jolor# normall! stoc.s 11# 12# or 1( cases o+ BJ)H each ee.- 9or each case that =ohn sells# he receives a pro+it o+ 3(5- Li.e man! photo"raphic chemicals# BJ)H has a ver! short shel+ li+e# so i+ a case is not sol$ b! the en$ o+ the ee.# =ohn must $iscar$ it- ince each case costs =ohn 35H# he loses 35H +or ever! case that is not sol$ b! the en$ o+ the ee.- There is a probabilit! o+ /-45 o+ sellin" 11 cases# a probabilit! o+ /-(5 o+ sellin" 12 cases# an$ a probabilit! o+ /-2 o+ sellin" 1( cases&a, Jonstruct a $ecision table +or this problem- Inclu$e all con$itional values an$ probabilities in the table&b, hat is !our recommen$e$ course o+ action &c, I+ =ohn is able to $evelop BJ)H ith an in"re$ient that stabilies it so that it no lon"er has to be $iscar$e$# ho oul$ this chan"e !our recommen$e$ course o+ action olution: &a, e have the +olloin" $ecision table : T;J% 11 cases 12 cases 1( cases 'robabilit!
11 cases 11C3(5 3(?5 11C3(5 > 1C35H 3(2 11C3(5 > 2C35H 32*( /-45
T;J% ;LD 12 cases 11C3(5 3(?5 12C3(5 342/ 12C3(5 > 1C35H 3(H4 /-(5
1( cases 11C3(5 3(?5 12C3(5 342/ 1(C3(5 3455 /-2
&b, e have: 68&11 cases, &/-45,C&3(?5, &/-(5,C&3(?5, &/-2,C&3(?5, 3(?5 68&12 cases, &/-45,C&3(2, &/-(5,C&342/, &/-2,C&342/, 3(*-/5 68&1( cases, &/-45,C&32*(, &/-(5,C&3(H4, &/-2,C&3455, 3(41-25 Depen$in" on the 8aximie 6xpecte$ 8onetar! alue mo$el# =ohn shoul$ choose to sell 11 cases because it has the hi"hest 68-
Name: Le Duc Thinh ID: BABAIU14255 &c, I+ =ohn is able to $evelop BJ)H ith an in"re$ient that stabilies it so that it no lon"er has to be $iscar$e$# e have the $ecision table as +olloin": T;J% 11 cases 12 cases 1( cases 'robabilit!
11 cases 11C3(5 3(?5 11C3(5 3(?5 11C3(5 3(?5 /-45
T;J% ;LD 12 cases 11C3(5 3(?5 12C3(5 342/ 12C3(5 342/ /-(5
1( cases 11C3(5 3(?5 12C3(5 342/ 1(C3(5 3455 /-2
e have: 68&11 cases, &/-45,C&3(?5, &/-(5,C&3(?5, &/-2,C&3(?5, 3(?5 68&12 cases, &/-45,C&3(?5, &/-(5,C&342/, &/-2,C&342/, 34/4-25 68&1( cases, &/-45,C&3(?5, &/-(5,C&342/, &/-2,C&3455, 3411-25 In this situation# base$ on the 8aximie 6xpecte$ 8onetar! alue mo$el# =ohn shoul$ choose to sell 1( cases because o+ their hi"hest 68-
