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7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign
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MNS407 Management Science, Summer 1 2023
407 Week 3: Quiz#3 (Quiz) INSTRUCTOR
Karen Joiner
National University, La Jolla CA
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7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign
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This Quiz covers material in Chapter 13. You have one
attempt to submit your answers.
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matters! Make sure you had successfully completed the
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7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign
https://www.webassign.net/web/Student/Assignment-Responses/last?dep=31948011#question4538525_9 3/14
A real estate investor has the opportunity to purchase land currently zoned residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table.
State of Nature
Rezoning Approved Rezoning Not Approved
Decision Alternative
Purchase, 650 −200
Do not purchase, 0 0
(a) If the probability that the rezoning will be approved is 0.5, what decision is recommended?
purchase
do not purchase
What is the expected profit (in dollars)?
$
(b) The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows:
Let
H = High resistance to rezoning L = Low resistance to rezoning
What is the optimal decision strategy if the investor uses the option period to learn more about the resistance from area residents before making the purchase decision?
If high resistance H, d purchase. If low resistance L, d do not purchase.
If high resistance H, d do not purchase. If low resistance L, d purchase.
If high resistance H, d purchase. If low resistance L, d purchase.
s1 s2
d1
d2
P(H) = 0.55 P(s | H) = 0.14 P(s | H) = 0.86 P(L) = 0.45 P(s | L) = 0.94 P(s | L) = 0.06
1 2
1 2
1 2
2 1
1 1
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If high resistance H, d do not purchase. If low resistance L, d do not purchase.
(c) If the option will cost the investor an additional $10,000, should the investor purchase the option? Why or why not? What is the maximum (in dollars) that the investor should be willing to pay for the option?
The investor ---Select--- purchase this option, as the payoff of the investing in it is ---Select--- $10,000 dollars. In general, the cost of the option can be, at most, $
in order for its payoff to break even with its cost of investing in it.
Show My Work (Optional)
2 2
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The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.
Decision Alternative
States of Nature
260 110 35
110 110 85
The probabilities for the states of nature are and
(a) What is the optimal decision strategy if perfect information were available?
If then ? ; If then ? ; If then ? .
(b) What is the expected value for the decision strategy developed in part (a)?
(c) Using the expected value approach, what is the recommended decision without perfect information? What is its expected value?
The recommended decision without perfect information is ? .
(d) What is the expected value of perfect information?
Show My Work (Optional)
s1 s2 s3
d1
d2
P(s ) = 0.65,1 P(s ) = 0.15,2 P(s ) = 0.20.3
s1 s2 s3
EV =
EVPI =
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A development corporation purchased land that will be the site of a new luxury condominium complex. Management is considering a six month market research study designed to learn more about potential market acceptance of the condominium project. Management anticipates that, if conducted, the market research study will provide one of the following two results.
1. Favorable report (F): A significant number of the individuals contacted express interest in purchasing a condominium.
2. Unfavorable report (U): Very few of the individuals contacted express interest in purchasing a condominium.
After deciding whether to conduct the market research study, they have the following two decision alternatives.
Following this, a chance event concerning the demand for the condominiums has two states of nature.
The payoff table showing profit is as follows.
Decision Alternative
States of Nature
300 900
1200 600
(a) Show the decision tree.
d = a small complex with 30 condominiums d = a medium complex with 60 condominiums
1
2
s = strong demand for the condominiums s = weak demand for the condominiums 1
2
s1 s2
d1
d2
3. [–/0.9 Points] ASWMSCI15 13.E.016.DETAILS
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(b) Use the following probabilities.
What is the optimal decision strategy?
ℹ
1
Market Research
No Market Research
F
U
d1
d2
d1
d2
d1
d2
s1
s2
s1
s2
s1
s2
s1
s2
s1
s2
s1
s2
2
3
4
5
6
7
8
9
10
11
P(F) = 0.58 P(U) = 0.42
P(s |F) = 0.591 P(s |F) = 0.412
P(s |U) = 0.161 P(s |U) = 0.842
P(s ) = 0.411 P(s ) = 0.592
Decision Tree Description
7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign
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Conduct the market research. If it is favorable, choose decision d . If it is unfavorable, choose
decision d .
Conduct the market research. If it is favorable, choose decision d . If it is unfavorable, choose
decision d .
Don't conduct the market research. Choose decision d .
Don't conduct the market research. Choose decision d .
Show My Work (Optional)
What does sensitivity analysis consider?
how changes in various aspects of the problem affect the recommended decision alternative
how changes in the number of states of nature can impact the recommended decision
how sensitive the decision maker is to risk
None of these are correct.
Show My Work (Optional)
1
2
2
1
1
2
4. [–/0.9 Points] CAMMIMS16 13.TB.035.DETAILS
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If P(high) = 0.38, P(low) = 0.62, P(favorable | high) = 0.88, and P(unfavorable | low) = 0.56, then what is P(favorable)?
0.1200
0.3344
0.3800
0.6072
Show My Work (Optional)
The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature.
Decision Alternative
States of Nature
240 90 15
90 90 65
Suppose that the decision maker obtained the probabilities and Use the expected value approach to determine the optimal decision.
EV(d ) =
EV(d ) =
The optimal decision is ? .
Show My Work (Optional)
s1 s2 s3
d1
d2
P(s ) = 0.65, P(s ) = 0.15,1 2 P(s ) = 0.20.3
1
2
5. [–/0.9 Points] CAMMIMS16 13.TB.037.DETAILS
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A paint company has three sources for buying bright red pigment for its paints: Vietnam, Taiwan, and Thailand. Unfortunately, the pigment is made from a bush whose annual growth is heavily dependent upon the amount of rainfall during the growing season. The following tables show probabilities and prices for wet, dry, and normal growing seasons.
Probabilities
Wet Dry Normal
Vietnam 0.5 0.2 0.3
Taiwan 0.6 0.3 0.1
Thailand 0.4 0.4 0.2
Price/Pound ($)
Wet Dry Normal
Vietnam 0.96 1.14 1.02
Taiwan 0.84 1.21 0.97
Thailand 0.91 1.17 1.06
What country should the company select?
Taiwan
Thailand
Vietnam
What is the expected value (price) associated with it?
Show My Work (Optional)
7. [–/0.9 Points] CAMMIMS16 13.TB.073.DETAILS
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The operations manager for a water taxi company wants to decide whether to purchase a small, medium, or large new boat for the company. The manager estimates that the annual profits (in thousands of dollars) will vary depending upon whether passenger demand is low, moderate, or high, as shown in the following table.
Demand
Boat Low Medium High
Small 51 63 71
Medium 38 83 92
Large 20 49 119
Probability 0.3 0.3 0.4
If the company uses the expected value approach, which size boat will it decide to purchase?
small
medium
large
none
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8. [–/0.9 Points] CAMMIMS16 13.TB.058.DETAILS
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A decision maker has developed the decision tree shown in the following figure.
How sensitive is the choice between N and P to the probabilities of states of nature U and V, and which would you choose? (Let Round your answer to four decimal places.)
The decision maker should choose N if p is greater than or equal to and less than or
equal to .
Show My Work (Optional)
ℹ
p = P(U).
Decision Tree Description
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The operations manager for a water taxi company wants to decide whether to purchase a small, medium, or large new boat for the company. The manager estimates that the annual profits (in thousands of dollars) will vary depending upon whether passenger demand is low, moderate, or high, as shown in the following table.
Demand
Boat Low Medium High
Small 47 62 67
Medium 41 79 88
Large 23 53 121
Probability 0.25 0.3 0.45
What is the expected value of perfect information?
$13,800
$18,800
$76,100
$94,900
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10. [–/0.9 Points] CAMMIMS16 13.TB.061.DETAILS
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Which of the following methods for decision making best protects the decision maker from undesirable results?
the optimistic approach
minimax regret
the conservative approach
minimum regret
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