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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

https://www.webassign.net/web/Student/Assignment-Responses/last?dep=31948011#question4538525_9 2/14

This Quiz covers material in Chapter 13. You have one

attempt to submit your answers.

The way that you write your answers matters! Syntax

matters! Make sure you had successfully completed the

"Getting Started in Web Assign for Mathematics" training

quiz in Module 1. This training quiz makes it clear how to

provide answers that the WebAssign system understands

for homework, quizzes, and the �nal.

Assignment Submission &

Scoring

Assignment Submission

For this assignment, you submit

answers by question parts. The

number of submissions remaining for

each question part only changes if

you submit or change the answer.

Assignment Scoring

Your last submission is used for your

score.

Instructions

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

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

2 1

1 1

1. [–/0.9 Points] ASWMSCI15 13.E.021.DETAILS

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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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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

7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign

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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

P(s ) = 0.65,1 P(s ) = 0.15,2 P(s ) = 0.20.3

s1 s2 s3

EV =

EVPI =

2. [–/0.9 Points] ASWMSCI15 13.E.014.DETAILS

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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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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

s = strong demand for the condominiums s = weak demand for the condominiums 1

s1 s2

3. [–/0.9 Points] ASWMSCI15 13.E.016.DETAILS

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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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(b) Use the following probabilities.

What is the optimal decision strategy?

ℹ

Market Research

No Market Research

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 .

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.

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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 ) =

The optimal decision is ? .

Show My Work (Optional)

s1 s2 s3

P(s ) = 0.65, P(s ) = 0.15,1 2 P(s ) = 0.20.3

5. [–/0.9 Points] CAMMIMS16 13.TB.037.DETAILS

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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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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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7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign

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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

Show My Work (Optional)

8. [–/0.9 Points] CAMMIMS16 13.TB.058.DETAILS

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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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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

9. [–/1 Points] CAMMIMS16 13.TB.069.DETAILS

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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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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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7/11/23, 1:08 AM 407 Week 3: Quiz#3 - MNS407 Management Science, Summer 1 2023 | WebAssign

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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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