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MNS407 Management Science, Fall 2024

407 Week 3: Homework#3 (Homework)
INSTRUCTOR

Vahid Keyhani
National University, La Jolla CA

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QUESTION

POINTS

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SAT, NOV 16, 2024

11:59 PM PST

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This homework covers material in Chapter 13. You have 5 attempts to get this right. Feel free to submit until you are

satis�ed with the results. Do not forget to use the practice button and help hints in the process.

Remember you have taken the “Getting Started in Web Assign for Mathematics” quiz in week one because the way

you write your answers matters for homework, quizzes, and the �nal. Be careful with syntax again.

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11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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Amy Lloyd is interested in leasing a new car and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36 month lease with no down payment due at the time
of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional
miles follow:

Dealer
Monthly

Cost
Mileage

Allowance
Cost per

Additional Mile

Dealer A $294 36,000 $0.15

Dealer B $305 45,000 $0.20

Dealer C $320 54,000 $0.15

Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision
she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease
options. For example, she figures that the Dealer A lease will cost her $10,584 if he drives 12,000 miles per year, $11,934 if he drives 15,000 miles per year, or $13,284 if he drives 18,000 miles per year.

(a) What is the decision, and what is the chance event?

The decision is to choose —Select— . There are ? alternatives. The chance event is —Select— . There are ? possible outcomes.

(b) Construct a payoff table. (Enter your answers in $).

Dealer
Annual Miles Driven

12,000 15,000 18,000

Dealer A $10,584 $11,934 $13,284

Dealer B $ $ $

Dealer C $ $ $

(c) If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches?

The recommended decision using the optimistic approach is —Select— . The recommended decision using the conservative approach is —Select— . The recommended decision using the
minimax regret approach is —Select— .

(d) Suppose that the probabilities that Amy drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What option should Amy choose using the expected value approach?

EV(Dealer A) = $

EV(Dealer B) = $

EV(Dealer C) = $

The best decision is —Select— .

(e) Develop a risk profile for the decision selected in part (d). What is the most likely cost, and what is its probability? (Submit a file with a maximum size of 1 MB.)

1. [–/1.14 Points] ASWMSCI15 13.E.004.DETAILS MY NOTES PRACTICE ANOTHER

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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Choose File No file chosen

This answer has not been graded yet.

(f) Suppose that after further consideration Amy concludes that the probabilities that she will drive 12,000, 15,000, and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What decision should Amy
make using the expected value approach?

EV(Dealer A) = $

EV(Dealer B) = $

EV(Dealer C) = $

The best decision is —Select— .

Show My Work

(Optional)

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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An airline decided to offer direct service from City A to City B. Management must decide between a full price service using the company’s new fleet of jet aircraft and a discount service using smaller capacity
commuter planes. It is clear that the best choice depends on the market reaction to the service the airline offers. Management developed estimates of the contribution to profit for each type of service based
upon two possible levels of demand for service to the airline: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars).

Service
Demand for Service

Strong Weak

Full price $950 −$510

Discount $680 $330

(a) What is the decision to be made, what is the chance event, and what is the consequence for this problem?

The decision to be made is —Select— . The chance event is —Select— . The consequence is —Select— .

How many decision alternatives are there?

How many outcomes are there for the chance event?

(b) If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

The recommended decision using the optimistic approach is the —Select— service. The recommended decision using the conservative approach is the —Select— service. The recommended
decision using the minimax regret approach is the —Select— service.

(c) Suppose that management of the airline believes that the probability of strong demand is 0.7 and the probability of weak demand is 0.3. Use the expected value approach to determine an optimal
decision. (Enter your answers in thousands of dollars.)

EV(full) $ thousands

EV(discount) $ thousands

The optimal decision is the —Select— service.

(d) Suppose that the probability of strong demand is 0.8 and the probability of weak demand is 0.2. What is the optimal decision using the expected value approach? (Enter your answers in thousands of
dollars.)

EV(full) $ thousands

EV(discount) $ thousands

The optimal decision is the —Select— service.

(e) Use graphical sensitivity analysis to determine the range of demand probabilities for which each of the decision alternatives has the largest expected value. (Round your answer to four decimal places.)

If the probability of strong demand falls below , the —Select— service is the best choice. If the probability of strong demand is greater than , the —Select—
service is the best choice.

2. [–/1.14 Points] ASWMSCI15 13.E.009.DETAILS MY NOTES PRACTICE ANOTHER

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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Show My Work

(Optional)

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the
skipped part.

Tutorial Exercise
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

230 80 5

80 80 55

(a) Construct a decision tree for this problem.

(b) If the decision maker knows nothing about the probabilities of the three states of nature, what is the recommended decision using the optimistic, conservative, and minimax regret approaches?

Show My Work

(Optional)

s1 s2 s3

d1

d2

3. [–/1.14 Points] ASWMSCI15 13.E.001.MI.SA.DETAILS MY NOTES PRACTICE ANOTHER

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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Investment advisors estimated the stock market returns for four market segments: computers, financial, manufacturing, and pharmaceuticals. Annual return projections vary depending on whether the
general economic conditions are improving, stable, or declining. The anticipated annual return percentages for each market segment under each economic condition are as follows.

Economic Condition

Market Segment Improving Stable Declining

Computers 11 2 −4

Financial 8 4 −3

Manufacturing 6 5 −2

Pharmaceuticals 6 4 −1

(a) Assume that an individual investor wants to select one market segment for a new investment. A forecast shows improving to declining economic conditions with the following probabilities: improving
(0.2), stable (0.5), and declining (0.3). What is the preferred market segment for the investor?

Computers

Financial

Manufacturing

Pharmaceuticals

What is the expected return percentage of the preferred market segment?

%

(b) At a later date, a revised forecast shows a potential for an improvement in economic conditions. New probabilities are as follows: improving (0.4), stable (0.4), and declining (0.2). What is the preferred
market segment for the investor based on these new probabilities?

Computers

Financial

Manufacturing

Pharmaceuticals

What is the expected return percentage of the preferred market segment?

%

Show My Work

(Optional)

4. [–/1.14 Points] ASWMSCI15 13.E.006.MI.DETAILS MY NOTES PRACTICE ANOTHER

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The
Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting
before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision concerning the type of grapes to plant difficult. Three possibilities
are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only
two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine it was necessary to assess four probabilities. With the help of some forecasts in industry publications
management made the following probability assessments.

Chardonnay Demand
Riesling Demand

Weak Strong

Weak 0.05 0.50

Strong 0.25 0.20

Revenue projections show an annual contribution to profit of $30,000 if Seneca Hill only plants Chardonnay grapes and demand is weak for Chardonnay wine, and $80,000 if the company only plants
Chardonnay grapes and demand is strong for Chardonnay wine. If Seneca Hill only plants Riesling grapes, the annual profit projection is $35,000 if demand is weak for Riesling grapes and $55,000 if demand
is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are as shown in the following table.

Chardonnay Demand
Riesling Demand

Weak Strong

Weak $32,000 $50,000

Strong $36,000 $70,000

(a) What is the decision to be made, what is the chance event, and what is the consequence?

The decision to be made is —Select— . The chance event is —Select— . The consequence is —Select— .

Identify the alternatives for the decisions and the possible outcomes for the chance events.

The alternatives for the decisions are —Select— . The possible outcomes for the chance events are —Select— .

(b) Develop a decision tree. (Enter monetary values in thousands and percentages in decimal form.)

Decision Tree Description

5. [–/1.14 Points] ASWMSCI15 13.E.013.DEFECTIVEDETAILS MY NOTES PRACTICE ANOTHER

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(c) Use the expected value approach to recommend which alternative Seneca Hill Winery should follow in order to maximize expected annual profit.

EV(Plant Chardonnay)

EV(Plant both grapes)

EV(Plant Riesling)

The best decision is to plant —Select— grapes.

(d) Suppose management is concerned about the probability assessments when demand for Chardonnay wine is strong. Some believe it is likely for Riesling demand to also be strong in this case. Suppose
the probability of strong demand for Chardonnay and weak demand for Riesling is 0.05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is 0.40. How does this
change the recommended decision? Assume that the probabilities when Chardonnay demand is weak are still 0.05 and 0.50.

EV(Plant Chardonnay)

EV(Plant both grapes)

EV(Plant Riesling)

The best decision is to plant —Select— grapes.

(e) Other members of the management team expect the Chardonnay market to become saturated at some point in the future, causing a fall in prices. Suppose that the annual profit projections fall to
$50,000 when demand for Chardonnay is strong and Chardonnay grapes only are planted. Using the original probability assessments, determine how this change would affect the optimal decision.

EV(Plant Chardonnay)

EV(Plant both grapes)

EV(Plant Riesling)

The best decision is to plant —Select— grapes.

ℹ

1

2

3

4

Plant Chardonnay

Plant both grapes

Plant Riesling

Weak for Chardonnay

Strong for Chardonnay

Weak Chardonnay, Weak Riesling

Weak Chardonnay, Strong Riesling

Strong Chardonnay, Weak Riesling

Strong Chardonnay, Strong Riesling

Weak for Riesling

Strong for Riesling

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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Show My Work

(Optional)

The following payoff table shows the profit for a decision problem with two states of nature and two decision alternatives.

State of Nature

Decision Alternative

13 4

7 6

(a) Use graphical sensitivity analysis to determine the range of probabilities of state of nature for which each of the decision alternatives has the largest expected value.

–?– is optimal for –?– is optimal for

(b) Suppose and What is the best decision using the expected value approach?

The best decision is –?– with an expected value of .

(c) Perform sensitivity analysis on the payoffs for decision alternative Assume the probabilities are as given in part (b), and find the range of payoffs under states of nature and that will keep the
solution found in part (b) optimal.

As long as the payoff for is –?– , then will be optimal.

As long as the payoff for is –?– , then will be optimal.

Is the solution more sensitive to the payoff under state of nature or

s

s

Show My Work

(Optional)

s1 s2

d1

d2

s1

p(s ) ≤ ;1 p(s ) ≥ .1

P(s ) = 0.21 P(s ) = 0.8.2

d .1 s1 s2

s1 d2

s2 d2

s1 s ?2

1

2

6. [–/1.16 Points] CAMMIMS16 13.E.008.DETAILS MY NOTES PRACTICE ANOTHER

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the
skipped part.

Tutorial Exercise
Suppose that you are given a decision situation with three possible states of nature: The prior probabilities are With sample information I,

and Compute the revised or posterior probabilities:

Show My Work

(Optional)

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s , s , and s .1 2 3 P(s ) = 0.5, P(s ) = 0.4, and P(s ) = 0.1.1 2 3
P(I|s ) = 0.1, P(I|s ) = 0.05,1 2 P(I|s ) = 0.2.3 P(s |I), P(s |I), and P(s |I).1 2 3

7. [–/1.14 Points] ASWMSCI15 13.E.023.MI.SA.DETAILS MY NOTES PRACTICE ANOTHER

11/9/24, 8:21 PM 407 Week 3: Homework#3 – MNS407 Management Science, Fall 2024 | WebAssign

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