Name: Le Duc Thinh ID: BABAIU14255 QUANTITATIVE QUANTITATIVE METHODS MET HODS FOR BUSINESS ASSI!NMENT: DE"ISION TREE ##5: The physicians in Problem 3–34 have been approached by a market
research frm that oers to perorm a study o the market at a ee o $5!!!" The market market researchers researchers claim their e#perience enables them to use ayes% theorem to make the ollo&in' statements o probability: • • • • • •
Probability Probability Probability Probability Probability Probability
o o o o o o
a avorable market 'iven a avorable study ( !")* an unavorable market 'iven a avorable study ( !"+) a avorable market 'iven an unavorable study ( !"++ an unavorable market 'iven an unavorable study ( !"), a avorable research study ( !"55 an unavorable research study ( !"45
-a. /evelop a ne& decision tree or the medical proessionals to re0ect the options no& open &ith the market study" -b. 1se the 2 approach to recommend a strate'y" -c. hat is the e#pected value o sample inormation6 7o& much mi'ht the physicians be &illin' to pay or a market study6 -d. 8alculate the e9ciency o this sample inormation" inormation" S$%u&i$n:
-b. – iven avorable survey results &e have: 2-node *. ( 2-construct ; positive survey. ( -!")*.<-$,5!!!. = -!"+).<-–$45!!!. -!"+).<-–$45!!!. ( $>,)!! The 2 o the situation that the clinic is not constructed in this case is – $5!!!" Thus i the survey results are avorable they should construct the clinic" – iven ne'ative survey results &e have: 2-node 3. ( 2-construct ; ne'ative survey. ( -!"++.<-$,5!!!. = -!"),.<-–$45!!!. -!"),.<-–$45!!!. ( –$*,>!! The 2 o the situation that the clinic is not constructed in this case is – $5!!!" Thus i the survey results are ne'ative they should not construct the clinic" – The e#pected value o conductin' the market survey is: 2-node +. ( 2-conduct survey. ( -!"55.<-$>,)!!. = -!"45.<-–$5!!!. ( $3>+4!
– ? the market survey is not conducted &e have: 2-node 4. ( -!"5.<-$+!!!!!. = -!"5.<-–$4!!!!. ( $3!!!! The 2 o the situation that the clinic is not constructed in this case is $!" Thus constructin' the clinic is the best choice 'iven that the market survey is not perormed" Thereore survey."
the survey should be used since 2 -conduct survey. @ 2 -no
? it is avorable construct the clinic" ? it is unavorable don%t
construct the clinic" -c. e have: 2A? ( -2 &ith sample inormation = cost. – -2 &ithout sample inormation. ( -$3>+4! = $5!!!. – $3!!!! ( $+++4! Thus the physicians &ould pay up to $+++4! or the survey" -d. e have the decision table as ollo&in': /28?A?BC DET2FCDT?2 8onstruct clinic /o nothin' ith perect inormation Probability
e have: 2-construct clinic. ( -!"5.<-$+!!!!!. = -!"5.<-–$4!!!!. ( $3!!!! 2-do nothin'. ( -!"5.<-$!. = -!"5.<-$!. ( $! est alternative or avorable and unavorable market is constructin' the clinic &ith a payo o $+!!!!! and not construct the clinic &ith a payo o $! respectively" e have: 2-&ith perect inormation. ( -!"5.<-$+!!!!!. = -!"5.<-$!. ( $5!!!! 2P? ( 2-&ith perect inormation. – a#imum 2 -&ithout perect inormation. ( $5!!!! – $3!!!! ( $*!!!!
29ciency o sample inormation (
EVSI EVPI
×100
(
$ 11,140 $ 20,000
× 100
55"IJ Thus the market survey is only 55"IJ as e9cient as perect inormation" #41: D fnancial advisor has recommended t&o possible mutual unds or
investment: Gund D
(
and Gund " The return that &ill be achieved by each o these depends on &hether the economy is 'ood air or poor" D payo table has been constructed to illustrate this situation: -a. /ra& the decision tree to represent this situation" -b. Perorm the necessary calculations to determine &hich o the t&o mutual unds is better" hich one should you choose to ma#imiKe the e#pected value6 -c. Auppose there is Luestion about the return o Gund D in a 'ood economy" ?t could be hi'her or lo&er than $+!!!!" hat value or this &ould cause a person to be indierent bet&een Gund D and Gund -i"e" the 2s &ould be the same.6 ?C2AT2CT Gund D Gund Probability
BB/ 28BCBM $+!!!! $>!!! !"*
ATDT2 BG CDT1F2 GD?F 28BCBM $*!!! $4!!! !"3
PBBF 28BCBM –$5!!! ! !"5
-b. e have: 2-und D. ( -!"*.<-$+!!!!. = -!"3.<-$*!!!. = -!"5.<-–$5!!!. ( $+!! 2-und . ( -!"*.<-$>!!!. = -!"3.<-$4!!!. = -!"5.<-$!. ( $*4!! 2-no investment. ( $! 7ence investin' in und is the best choice since it ma#imiKes the e#pected value" -c. Eet N -dollars. be the return o und D in a 'ood economy" e are indierent &hen the 2 o und D is the same as the 2 o und &hich is $*4!!" e have: 2-und D. ( 2-und . -!"*.<-N. = -!"3.<-$*!!!. = -!"5.<-–$5!!!. ( $*4!! -!"*.
or the t&o unds to be eLually desirable based on the e#pected values" #42: Oim Aellers is thinkin' about producin' a ne& type o electric raKor or
men" ? the market &ere avorable he &ould 'et a return o $+!!!!! but i the market or this ne& type o raKor &ere unavorable he &ould lose $>!!!!" Aince Fon ush is a 'ood riend o Oim Aellers Oim is considerin' the possibility o usin' ush arketin' Fesearch to 'ather additional inormation
about the market or the raKor" Fon has su''ested that Oim either use a survey or a pilot study to test the market" The survey &ould be a sophisticated Luestionnaire administered to a test market" ?t &ill cost $5!!!" Dnother alternative is to run a pilot study" This &ould involve producin' a limited number o the ne& raKors and tryin' to sell them in t&o cities that are typical o Dmerican cities" The pilot study is more accurate but is also more e#pensive" ?t &ill cost $*!!!!" Fon ush has su''ested that it &ould be a 'ood idea or Oim to conduct either the survey or the pilot beore Oim makes the decision concernin' &hether to produce the ne& raKor" ut Oim is not sure i the value o the survey or the pilot is &orth the cost" Oim estimates that the probability o a successul market &ithout perormin' a survey or pilot study is !"5" Gurthermore the probability o a avorable survey result 'iven a avorable market or raKors is !"I and the probability o a avorable survey result 'iven an unsuccessul market or raKors is !"*" ?n addition the probability o an unavorable pilot study 'iven an unavorable market is !", and the probability o an unsuccessul pilot study result 'iven a avorable market or raKors is !"* -a. /ra& the decision tree or this problem &ithout the probability values" -b. 8ompute the revised probabilities needed to complete the decision and place these values in the decision tree" -c. hat is the best decision or Oim6 1se 2 as the decision criterion"
-b. Eet G 1 GA 1A GP and 1P respectively be the avorable market unavorable market avorable survey unavorable survey avorable pilot study and unavorable pilot study" e have: •
P ( FM ∨ FS ) × P ( FS )+ P ¿ P ( FM ∨ FS ) × P ( FS )
¿
!"I
0.78 × P ( FS )
(
(@ P-GA.
( !"45 P-1A. ( !"55
0.78 × P ( FS )+ 0.27 ×( 1 − P ( FS ) )
FM |UP ) × P ( UP )
P-GP ; G.
(
P ( FM ∨ FP ) × P ( FP )+ P ¿ P ( FM ∨ FP ) × P ( FP )
¿ !")
(
0.89 × P FP
(
(@ P-GP.
( !"45 P-1P. ( !"55
(
0.89× P FP
)
)+ 0.18 × ( 1− P ( FP ))
-c. <1se survey: – iven avorable survey results &e have: 2-node 3. ( -!"I).<-$,5!!!. = -!"**.<-–$>5!!!. ( $5,)!! The 2 o the situation that the raKor is not produced in this case is – $5!!!" Thus i the survey results are avorable they should produce the raKor" – iven ne'ative survey results &e have: 2-node 4. ( -!"*I.<-$,5!!!. = -!"I3.<-–$>5!!!. ( –$*+)!! The 2 o the situation that the raKor is not produced in this case is – $5!!!" Thus i the survey results are unavorable they should not produce the raKor" – The e#pected value o conductin' the market survey is: 2-node +. ( 2-conduct survey. ( -!"45.<-$5,)!!. = -!"55.<-–$5!!!. ( $*4+>! <1se pilot study: – iven avorable study results &e have: 2-node 5. ( -!"),.<-$)!!!!. = -!"++.<-–$)!!!!. ( $>*4!! The 2 o the situation that the raKor is not produced in this case is – $*!!!!" Thus i the study results are avorable they should produce the raKor" – ? the study results is ne'ative &e have: 2-node >. ( -!"+).<-$)!!!!. = -!")*.<-–$)!!!!. ( –$5+*!! The 2 o the situation that the raKor is not produced in this case is – $*!!!!" Thus i the study results are unavorable they should not produce the raKor" – The e#pected value o conductin' the market survey is: 2-node *. ( 2-conduct pilot study.
( -!"45.<-$>*4!!. = -!"55.<-–$*!!!!. ( $+I!)! !!!!. ( $*!!!! The 2 o the situation that the raKor is not produced in this case is $!" Thus producin' the raKor is the best choice 'iven that the market survey and pilot study is not perormed" (@ Ao since 2 -conduct survey. @ 2-not conduct anythin'. @ 2-conduct pilot study. the survey should be used "
