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MNS407 Management Science, Fall 2024
407 Week 3: Quiz#3 (Quiz)
INSTRUCTOR
Vahid Keyhani
National University, La Jolla CA
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SUN, NOV 17, 2024
11:59 PM PST
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This Quiz covers material in Chapter 13. You have one attempt to submit your answers.
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Due Date
Instructions
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
1/13
What does sensitivity analysis consider?
how changes in the number of states of nature can impact the recommended decision
how changes in various aspects of the problem affect the recommended decision alternative
how sensitive the decision maker is to risk
None of these are correct.
Show My Work
(Optional)
1. [–/0.9 Points] CAMMIMS16 13.TB.035.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
2/13
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
400 1200
1600 800
(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
Decision Tree Description
2. [–/0.9 Points] ASWMSCI15 13.E.016.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
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(b) Use the following probabilities.
What is the optimal decision strategy?
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 .
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) = 0.59
P(U) = 0.41
P(s |F) = 0.581
P(s |F) = 0.422
P(s |U) = 0.171
P(s |U) = 0.832
P(s ) = 0.411
P(s ) = 0.592
1 2
2 1
1
2
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
4/13
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
3. [–/0.9 Points] ASWMSCI15 13.E.005.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
5/13
Which of the following methods for decision making best protects the decision maker from undesirable results?
the optimistic approach
minimum regret
the conservative approach
minimax regret
Show My Work
(Optional)
4. [–/0.9 Points] CAMMIMS16 13.TB.034.DETAILS MY NOTES
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
6/13
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
270 120 45
120 120 95
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 =
5. [–/0.9 Points] ASWMSCI15 13.E.014.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
7/13
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 48 60 71
Medium 43 77 91
Large 19 51 122
Probability 0.25 0.3 0.45
What is the expected value of perfect information?
$15,050
$20,800
$74,950
$95,750
Show My Work
(Optional)
6. [–/0.9 Points] CAMMIMS16 13.TB.061.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
8/13
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
7. [–/1 Points] CAMMIMS16 13.TB.069.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
9/13
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, 670 −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 purchase.
If high resistance H, d do not purchase. If low resistance L, d purchase.
If high resistance H, d do not purchase. If low resistance L, d do not purchase.
If high resistance H, d 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.
s1 s2
d1
d2
P(H) = 0.45 P(s | H) = 0.17 P(s | H) = 0.83
P(L) = 0.55 P(s | L) = 0.77 P(s | L) = 0.23
1 2
1 2
1 1
2 1
2 2
1 2
8. [–/0.9 Points] ASWMSCI15 13.E.021.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
10/13
Show My Work
(Optional)
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 0.94 1.12 1.05
Taiwan 0.84 1.25 0.99
Thailand 0.92 1.16 1.04
What country should the company select?
Vietnam
Thailand
Taiwan
What is the expected value (price) associated with it?
Show My Work
(Optional)
9. [–/0.9 Points] CAMMIMS16 13.TB.073.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
11/13
If P(high) = 0.31, P(low) = 0.69, P(favorable | high) = 0.85, and P(unfavorable | low) = 0.63, then what is P(favorable)?
0.1500
0.2635
0.3100
0.5188
Show My Work
(Optional)
10. [–/0.9 Points] CAMMIMS16 13.TB.037.DETAILS MY NOTES PRACTICE ANOTHER
11/7/24, 5:21 PM 407 Week 3: Quiz#3 – MNS407 Management Science, Fall 2024 | WebAssign
12/13
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 52 61 68
Medium 41 81 88
Large 23 47 120
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
Show My Work
(Optional)
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