Question Details
MGMT 2012 Introduction to Quantitative Method
s
Individual Assignment Graded Assignment Two S2
201617 Due April 15th â€“ 10
percent Final Grade
Students should note that this assignment should su
bmitted in a Word document.
Question 1A
Assume the following payoffs are
profits
.
Payoffs
states of nature
Decision
alternatives
1
2
3
A
50
75
30
B
35
55
60
C
40
50
(a)
Which alternative should the firm choose under the
maximax criterion?
(1 mark)
(b)
Which option should the firm choose under the maxim
in criterion?
(1 mark)
(c)
Which option should the firm choose under the LaPla
ce criterion?
(2 marks)
(d)
Which option should the firm choose with the Hurwic
z criterion with
Î±
= 0.4?
(2 marks)
(e)
Using a minimax regret approach, what alternative s
hould the firm choose?
(4 marks)
(f)
Probabilities of 0.25, 0.35, and 0.40 have been ass
igned
.
Using expected monetary
values, what option should be chosen and what is th
at optimal expected value?
(4
marks)
(g)
What is the most that the firm should be willing
to pay for additional information? Use
Expected Regret
(3 marks)
(h)
Use the alternative method to verify EVPI
(3 marks)
Question 1B
Assume now that the pay offs are
costs
answer the following
:
(a)
Using an optimistic approach (maximax), which optio
n would you choose? 1 mark
(b)
Using a pessimistic approach (maximin), which optio
n would you choose?1 mark
(c)
If you are a LaPlace decision maker, which option w
ould you choose? 2 marks
(d)
If you are a Hurwicz decision maker, which option w
ould you choose with
Î±
= 0.4?1
mark
(e)
Using a minimax regret approach, which option would
you choose? 4 marks
(f)
Using the same probabilities of 0.25, 0.35, and 0
.40 for possible states of nature
respectively
,
which decision alternative will
minimise
the expected
costs?
What are the
expected annual costs associated with that recommen
dation? 4 marks
g) What is the most the firm should be wil
ling to pay to obtain further (perfect)
information (EVPI)? 3 marks
h) Use the alternative method to verify EVP
I
(3 marks
Question 2
A farmer in the Blue Mountains area of Jamaica want
s to decide on the crop to plant next season.
He wants to plant either ganja or coffee for export
to the USA but need some help. He knows
that if he plants ganja and the weather in the USA
is predominantly cold he earns $10,000(US
per month. If the weather is warm he earns $16,000.
If he plants coffee and the weather is cold
he earns 13,000 and if the weather is warm he earns
$14000. In 40% of the years, the weather
was cold and in 60 % the weather was warm.
For $600, he could buy an expert weather forecast f
rom CWD consulting.
States of Nature with Profits ($)
Does not include forecast cost
Decision
Alternatives
Warm
weather(W)
Cold weather (C)
Ganja
$16,000
$10,000
Coffee
$14,000
$13000
Prior Probabilities
P(W) = 0.60
P(C) = .40
Conditional probability for a given state of nature
where forecasts are either Good (G) or bad
(B): That is: P (GW) = 0.80; P (BW) = 0.20;
P (G
C) = 0.10;
P (BC) = 0.90
After you have computed the revised probabilities r
ound to two decimal places
a)
Construct the appropriate decision tree to help the
farmer make the appropriate decisions.
This tree must be constructed in logical order with
labels and net payoffs
(5 marks
). It
also includes the revised probabilities (
5 marks
) (
10 marks
)
b)
Fold back the decision tree
(5 marks
) to determine the best strategy for the farmer; yo
u
must state this strategy (
1 mark
). What is the final expected profit?(
1 mark)(7 marks
)
c)
What is the expected value of sample information(EV
SI) the most that should be paid to
seismic testing firm for the test?(
1 mark
)
d)
Calculate the expected value of perfect information
(EVPI) the most that should be paid
CWD for prediction of the uncertain outcomes.(
1 mark
)
e)
What is the efficiency of sample information?(
1 mark
)
Question 3
Data collected on the yearly demand for 50pound ba
gs of fertilizer at Wallace Garden Supply
are shown in the following table.
a)Estimate demand with a weighted moving average i
n which sales in the most recent year, next
most recent , most distant are given weights of 3,
2 and 1 respectively . Compute the MAD,
MSE and MPE for this method.(
six marks
)
b)Use exponential smoothing with a smoothing consta
nt of 0.2 to forecast the demand for
fertilizer. Assume that last periodâ€™s forecast for
year 1 is 5,000 bags to begin the procedure.
Which method do you think is best?. Is this an impr
ovement over the weighted average use
MAD alone( Six
marks)
c) Use regression analysis to estimate the line of
best fit(
eight marks
). Forecast the demand for
years 12 and 13.
Question four
A new project is to be completed. The following ac
tivities need to be completed in the order
shown, where times are in weeks.
Activity
Immediate
predecessors
Optimistic
time
Most
likely
time
Most
pessimistic
time
Variance
A

2
3
4
0.11111
B

2
4
6
0.44444
C
A,B
1
2
3
0.11111
D
B
1
3
5
0.44444
E
A
2
3
4
0.11111
F
C
1
4
7
1
G
E,F
2
2
2
0
H
D,F
2
5
8
1
I
G,H
1
3
5
0.44444
J
I
2
3
4
0.11111
You must use two decimal places at all times for ex
pected times when they are not integer
(you are not permitted to round off to integers).
(a)
Draw the activity network for this problem
(6 marks)
(b)
Determine the Expected Times.
(1 mark)
(c)
Determine the activity schedule (ES, EF, LS, and LF
) as well as slack.
(7 marks)
(d)
Determine and state the critical path for this proj
ect.
(1 mark)
(e)
What are the expected time and the variance of the
project?
(2 marks)
(f)
What is the probability that the project is complet
ed in 22 or fewer weeks
(1 mark)
(g)
What date should be set su
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