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BBA 405 ONLINE: Management Science: Decision Making Review
Your firm is considering two investment projects, A and B. Given the budget constraints,
you must chose either A or B, but not both.
Project A will provide a net return of either $400, $500, or $600, respectively, depending on
whether there will be a recession, normal conditions, or a boom. The figures for Project B
are $150, $300, or $700, respectively.
Forecasts indicate that, given the current trends in appropriate economic indicators in the
following year the chances are 20% that a recession will occur, 60% that the economic
conditions will stay as they are, and 20% that the economy will enjoy a boom.
1. Construct a payoff table. (10 points)
ORIGINAL TABLE:
Payoff Table
Event/Condition
Recession
Normal
Boom
A
$ 400
$ 500
$ 600
B
$ 150
$ 300
$ 700
Fi(Probabilities)
0.2
0.6
0.2
2. If there were an uncertain decision situation rather than one under risk, what would
your choice be under the condition of perfect optimism, perfect pessimism, optimism
at .6, equal likelihood, and minimization of regrets? (50 points)
Item
Answer
Reason
Perfect Optimism
(MXMX)
Rank: B, A
Project B has the maximum
best possible outcome.
Best
$ 600
$ 700
Perfect
Pessimism
(MXMN)
Rank: A, B
Project A has the best
outcome among the worst
payoffs
Worst
$ 400
$ 150
Optimism at α=
0,6 (Hurwitz
criterion)
REAL'SM
Rank: A, B
Project A maximizes the
sum of both the maximum
and minimum weighted
payoffs.
Optimism degree-0.6
Pessimism degree-0.4
A=(600*0.6) + (400*0.4) = 520
B= (700*0.6) + (150*0.4) = 480

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Equal Likelihood
(Laplace rule)
Rank: A, B
Project A has the highest
expected value.
A= (400*1/3) + (500*1/3) + (600*1/3) = 500
B= (150*1/3) + (300*1/3) + (700*1/3) =383.3
Minimizing
Regret
Rank: A, B
Project A minimizes the
maximum possible regret in
case any contingencies
occur.
Maximum regret
$ 600
$ 700
OVERAL CONCLUSION:
Project A will be better because it has the best outcome among the worst payoffs, maximizes the sum
of both the maximum and minimum weighted payoffs, has the highest expected value and minimizes
the maximum possible regret in case any contingencies occur.
3.What is the expected value (x) of each alternative? Which alternative must you choose from
this point of view? (10 points)
A= (400*0.2) + (500*0.6) + (600*0.2) = 500
B= (150*0.2) + (300*0.6) + (700*0.2) = 350
Rank: A, B
Investment A has the highest possible expected value.
4. Which project should be chosen on the basis of the calculation of coefficient of variation?
(20 points)
Coefficient of variation
COV =σ/ mean * 100%
Conditions
Probabilities
A
B
(p)
X*p
(X-x)
2
p
(X-x)
2
p
Recession
0.2
(400*0.2)=80
2000
(150*0.2)=30
8000
Normal
0.6
(500*0.6)=300
0
(300*0.6)=180
1500
Boom
0.2
(600*0.2)=120
2000
(700*0.2)=140
24500
X (mean)
500
350
Variance
4000
34000

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BBA 405 ONLINE: Management Science: Decision Making Review Your firm is considering two investment projects, A and B. Given the budget constraints, you must chose either A or B, but not both. Project A will provide a net return of either $400, $500, or $600, respectively, depending on whether there will be a recession, normal conditions, or a boom. The figures for Project B are $150, $300, or $700, respectively. Forecasts indicate that, given the current trends in appropriate economic indicators in the following year the chances are 20% that a recession will occur, 60% that the economic conditions will stay as they are, and 20% that the economy will enjoy a boom. 1. Construct a payoff table. (10 points) ORIGINAL TABLE: Payoff Table Event/Condition Recession Normal Boom A B Fi(Probabilities) $ 400 $ 150 0.2 $ 500 $ 300 0.6 $ 600 $ 700 0.2 2. If there were an uncertain decision s ...
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