Blockwood Inc. must decide what type of truck to purchase for its operations. Three options are considered: a small import truck, standard pickup, or large flatbed truck. Sales in the first year are expected to fall into one of four categories. A payoff table outlines the expected profits for each truck type across the different sales levels. The document asks to analyze and make a decision using various decision making criteria, including Laplace, Minimax, Maximin, Savage Minimax Regret, and Hurwicz criteria. It also considers incorporating probability assessments and the value of market research.
1 EPOMEECS407 Final Exam Do ALL problems .docxjeremylockett77
1
EPOM/EECS407 Final Exam
Do ALL problems Time allowed: 3 hrs
1. (10 points) A manufacturing plant produces specially crafted engines for high-performance
automobiles. If it takes 3 working days to produce the first engine and the learning curve is such that it
only takes an estimated 70% of the time (required to produce the first engine) to produce the second
engine, determine how long it will take for the plant to be able to produce 2 engines in one working
day.
Name:……………………………………………………
2
2. (10 points) An investment amount of $10M has to be raised through equity financing and debt
financing. The required debt ratio is 0.40 and the company tax rate is 35%.
a) The current market price of the company’s common stock is $50 and the current dividend is $5
and the dividend is expected to grow at 5% annual rate. The floating cost of issuing a common
stock is 10%. Preferred stocks of $100 par value with 10% fixed annual dividend can also be
issued at 8% floating cost. If the required proportion of funds from retained earnings to common
stocks to preferred stocks are 0.4:0.2:0.4 respectively, what is the cost of equity?
b) Bank loans at 12% annual interest. Also, the company issues 20-year bonds that pay the equivalent
of 9.5% yield to maturity. If the required ratio of funds raised through these two methods of debt
financing is 0.6:0.4 what is the cost of debt?
c) From (a) and (b), what is the cost of capital (WACC)?
3
20000 40000 60000 80000 100000
5
5
10
15
20
25
3. (15 points) EECS Corporation has identified six investment opportunities that will last 1 year. The firm
draws up a list of all potentially acceptable projects, and computes their IRR and PW at 8.5% MARR as
shown below.
Project Initial Investment IRR PW(8.5%) ($)
1 17,000 8% 1300
2 12,000 10% 1120
3 15,000 5% 600
4 20,000 20% 3800
5 10,000 7% 720
6 16,000 15% 1700
a) If the marginal cost of capital for additional funds is 8% for $40,000 and 9% for the next 60,000
and the lending rate (if the company wants to lend their money) is 6% Assume that the company
has an investment budget of (i) $60,000 on hand and (ii) $0 on hand, and that there is no partial
project investment, what is the best investment strategy and MARR in each case? (Note in both
cases, additional borrowing is allowed if it is beneficial to do so.)
Draw an Investment Opportunity Schedule (IOS) and Marginal Cost of Capital (MCC) below.
4
3b) Again with the firm budget of $80,000 (no additional borrowing, allowed) formulate (but DO NOT
solve) an integer programming model to help determine an optimal portfolio of the above projects
based on maximizing the present worth at 8.5%. Also, the following conditions must be observed.
Projects1, 4 and 6 are mutually exclusive, and projec ...
mean, variance, and standard deviation of a
discrete probability distribution,binomial probability distribution,hypergeometric probability distribution,Poisson probability distribution.
You can use a calculator to do numerical calculations. No graphing.docxjeffevans62972
You can use a calculator to do numerical calculations. No graphing calculator is allowed. Please DO NOT USE ANY COMPUTER SOFTWARE to solve the problems.
1. (a) What is an assignment problem? Briefly discuss the decision variables, the objective function and constraint requirements in an assignment problem. Give a real world example of the assignment problem.
(b) What is a diet problem? Briefly discuss the objective function and constraint requirements in a diet problem. Give a real world example of a diet problem.
(c) What are the differences between QM for Windows and Excel when solving a linear programming problem? Which one you like better? Why?
(d) What are the dual prices? In what range are they valid? Why are they useful in making recommendations to the decision maker? Give a real world example.
Answer Questions 2 and 3 based on the following LP problem.
Let P1 = number of Product 1 to be produced
P2 = number of Product 2 to be produced
P3 = number of Product 3 to be produced
P4 = number of Product 4 to be produced
Maximize 80P1 + 100P2 + 120P3 + 70P4 Total profit
Subject to
10P1 + 12P2 + 10P3 + 8P4 ≤ 3200 Production budget constraint
4P1 + 3P2 + 2P3 + 3P4 ≤ 1000 Labor hours constraint
5P1 + 4P2 + 3P3 + 3P4 ≤ 1200 Material constraint
P1 > 100 Minimum quantity needed for Product 1 constraint
And P1, P2, P3, P4 ≥ 0 Non-negativity constraints
The QM for Windows output for this problem is given below.
Linear Programming Results:
Variable
Status
Value
P1
Basic
100
P2
NONBasic
0
P3
Basic
220
P4
NONBasic
0
slack 1
NONBasic
0
slack 2
Basic
160
slack 3
Basic
40
surplus 4
NONBasic
0
Optimal Value (Z)
34400
Original problem w/answers:
P1 P2 P3 P4 RHS Dual
Maximize
80 100 120 70
Constraint 1
10 12 10 8 <= 3200 12
Constraint 2 4 3 2 3 <= 1000 0
Constraint 3 5 4 3 3 <= 1200 0
Constraint 4 1 0 0 0 >= 100 -40
Solution
-> 100 0 220 0 Optimal Z-> 34400
Ranging Results:
Variable
Value
Reduced Cost
Original Val
Lower Bound
Upper Bound
P1
100
0
80
-Infinity
120
P2
0
44
100
-Infinity
144
P3
220
0
120
87.5
Infinity
P4
0
26
70
-Infinity
96
Constraint
Dual Value
Slack/Surplus
Original Val
Lower Bound
Upper Bound
Constraint 1
12
0
3200
1000
3333.333
Constraint 2
0
160
1000
840
Infinity
Constraint 3
0
40
1200
1160
Infinity
Constraint 4
-40
0
100
0
120
2. (a) Determine the optimal solution and optimal value and interpret their meanings.
(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.
3. (a) What are the ranges of optimali.
Economics 512 Homework IV (25 Points) Fall 2016 Do Pro.docxSALU18
Economics 512
Homework IV (25 Points)
Fall 2016
Do Problems 1, 2, 3, Below and 7-4, 7-10, 7-11, 9.3, 6-7, and Risk Analysis Questions
#3,5 and 8.
1. You make decorative stones for landscaping. A ton of coarse stones requires 2 hours
of crushing, 5 hours of sifting, and 8 hours of drying. A ton of fine stones requires 6
hours of crushing, 3 hours of sifting, and 2 hours of drying. The coarse stones sell for
$400 per ton. The fine stones sell for $800 per ton. In a work week your plant is capable
of 36 hours of crushing, 30 hours of sifting, and 40 hours of drying.
Use the graphical method first, to answer a. below. Then use your spreadsheet to verify
your answer and get the numbers you need for b. and c. For full credit for your graph,
draw the constraints and at least one iso-revenue line. Draw a circle or an arrow to
indicate the optimal point.
Determine:
a. How much of each kind of stones you should make to maximize your revenue.
b. How much revenue you'll make at the maximum.
c. How much it would be worth to you to get another hour of crushing time, sifting time,
or drying time.
2. You make three kinds of computers: Cheap, Good, and Deluxe. These sell for $1500,
$2000, and $2800. The Cheap model requires 3 hours for circuit board installation and 1
hour to fit the peripheral equipment. The Good model requires 1 hour for circuit boards
and 5 hours for peripherals. The deluxe model requires 3 hours for circuit boards and 2
hours for peripherals. You have 120 hours available for circuit board work and 60 hours
for fitting peripherals. Determine:
a. How much of each kind of computers you should make to maximize your revenue.
b. How much revenue you'll make at the maximum.
c. How much it would be worth to you to get another hour of circuit board assembly time
or peripheral fitting time.
This time you'll have to rely on your spreadsheet rather than the graph method. Why?
fr~cLJ c+f;"c-~ eD~-\- (Y\k{(IV'(-ZI~') 6\~+·~ e~.,-~
.......
Class A Class A Class A Class B Class B Beef Stocker
cotton milo wheat milo wheat cows steers
Units (acre) (acre) (acre) (acre) (acre) (head) (head)
Gross Margin $/UDlt S150 S100 $115 $85 $70 $205 $70 MAX
Class A land acre 1 1 1 0 0 0 0 LE
Class Bland acre 0 0 0 1 1 05 0 LE
Pasture acre 0 0 0 0 0 6 3 LE
Labor hour 4 3 2.5 3 25 6 1 LE
Rotation LimIt acre 1 0 0 0 0 0 0 LE
291
(c) lOx + 5y :::; 50
2y:::; 15
Jx:::; 9
x~O
v>O
(d) x + y:::; 40
2x + y:::; 60
Jx + Jy _ 60
x 0
y~O
7-2. Graph the fe~~sihle region defined h)' the following set ot Inequalities:
x + y.s; 40
2x + 4y :::; 100
3y .s; 60
x ~ 0
y~O
Using a graphic approach. determine thar poinr in the feasihle region (i.e.,
the values ot x and y) that minimizes e:\(h of the following ohtective
functions:
(<I) , x 3y
(b) z = 6x + 4y
7-3. Given the following linear progr,lm,
maximize n = 4Q .• + JQB
suhjeu to the followlIlg machine-time constraints:
Q" + 2QB .s;100
2Q" + ...
BUS 640 HOMEWORK Achievement Education--bus640homework.comclaric150
FOR MORE CLASSES VISIT
www.bus640homework.com
Week 1
Problem 1:
A generous university benefactor has agreed to donate a large amount of money for student scholarships. The money can be provided in one lump sum of $12 million in Year 0 (the current year), or in parts, in which $7 million can be provided at the end of Year 1, and another $7 million can be provided at the end of Year 2.
Describe your answer for each item below
1 EPOMEECS407 Final Exam Do ALL problems .docxjeremylockett77
1
EPOM/EECS407 Final Exam
Do ALL problems Time allowed: 3 hrs
1. (10 points) A manufacturing plant produces specially crafted engines for high-performance
automobiles. If it takes 3 working days to produce the first engine and the learning curve is such that it
only takes an estimated 70% of the time (required to produce the first engine) to produce the second
engine, determine how long it will take for the plant to be able to produce 2 engines in one working
day.
Name:……………………………………………………
2
2. (10 points) An investment amount of $10M has to be raised through equity financing and debt
financing. The required debt ratio is 0.40 and the company tax rate is 35%.
a) The current market price of the company’s common stock is $50 and the current dividend is $5
and the dividend is expected to grow at 5% annual rate. The floating cost of issuing a common
stock is 10%. Preferred stocks of $100 par value with 10% fixed annual dividend can also be
issued at 8% floating cost. If the required proportion of funds from retained earnings to common
stocks to preferred stocks are 0.4:0.2:0.4 respectively, what is the cost of equity?
b) Bank loans at 12% annual interest. Also, the company issues 20-year bonds that pay the equivalent
of 9.5% yield to maturity. If the required ratio of funds raised through these two methods of debt
financing is 0.6:0.4 what is the cost of debt?
c) From (a) and (b), what is the cost of capital (WACC)?
3
20000 40000 60000 80000 100000
5
5
10
15
20
25
3. (15 points) EECS Corporation has identified six investment opportunities that will last 1 year. The firm
draws up a list of all potentially acceptable projects, and computes their IRR and PW at 8.5% MARR as
shown below.
Project Initial Investment IRR PW(8.5%) ($)
1 17,000 8% 1300
2 12,000 10% 1120
3 15,000 5% 600
4 20,000 20% 3800
5 10,000 7% 720
6 16,000 15% 1700
a) If the marginal cost of capital for additional funds is 8% for $40,000 and 9% for the next 60,000
and the lending rate (if the company wants to lend their money) is 6% Assume that the company
has an investment budget of (i) $60,000 on hand and (ii) $0 on hand, and that there is no partial
project investment, what is the best investment strategy and MARR in each case? (Note in both
cases, additional borrowing is allowed if it is beneficial to do so.)
Draw an Investment Opportunity Schedule (IOS) and Marginal Cost of Capital (MCC) below.
4
3b) Again with the firm budget of $80,000 (no additional borrowing, allowed) formulate (but DO NOT
solve) an integer programming model to help determine an optimal portfolio of the above projects
based on maximizing the present worth at 8.5%. Also, the following conditions must be observed.
Projects1, 4 and 6 are mutually exclusive, and projec ...
mean, variance, and standard deviation of a
discrete probability distribution,binomial probability distribution,hypergeometric probability distribution,Poisson probability distribution.
You can use a calculator to do numerical calculations. No graphing.docxjeffevans62972
You can use a calculator to do numerical calculations. No graphing calculator is allowed. Please DO NOT USE ANY COMPUTER SOFTWARE to solve the problems.
1. (a) What is an assignment problem? Briefly discuss the decision variables, the objective function and constraint requirements in an assignment problem. Give a real world example of the assignment problem.
(b) What is a diet problem? Briefly discuss the objective function and constraint requirements in a diet problem. Give a real world example of a diet problem.
(c) What are the differences between QM for Windows and Excel when solving a linear programming problem? Which one you like better? Why?
(d) What are the dual prices? In what range are they valid? Why are they useful in making recommendations to the decision maker? Give a real world example.
Answer Questions 2 and 3 based on the following LP problem.
Let P1 = number of Product 1 to be produced
P2 = number of Product 2 to be produced
P3 = number of Product 3 to be produced
P4 = number of Product 4 to be produced
Maximize 80P1 + 100P2 + 120P3 + 70P4 Total profit
Subject to
10P1 + 12P2 + 10P3 + 8P4 ≤ 3200 Production budget constraint
4P1 + 3P2 + 2P3 + 3P4 ≤ 1000 Labor hours constraint
5P1 + 4P2 + 3P3 + 3P4 ≤ 1200 Material constraint
P1 > 100 Minimum quantity needed for Product 1 constraint
And P1, P2, P3, P4 ≥ 0 Non-negativity constraints
The QM for Windows output for this problem is given below.
Linear Programming Results:
Variable
Status
Value
P1
Basic
100
P2
NONBasic
0
P3
Basic
220
P4
NONBasic
0
slack 1
NONBasic
0
slack 2
Basic
160
slack 3
Basic
40
surplus 4
NONBasic
0
Optimal Value (Z)
34400
Original problem w/answers:
P1 P2 P3 P4 RHS Dual
Maximize
80 100 120 70
Constraint 1
10 12 10 8 <= 3200 12
Constraint 2 4 3 2 3 <= 1000 0
Constraint 3 5 4 3 3 <= 1200 0
Constraint 4 1 0 0 0 >= 100 -40
Solution
-> 100 0 220 0 Optimal Z-> 34400
Ranging Results:
Variable
Value
Reduced Cost
Original Val
Lower Bound
Upper Bound
P1
100
0
80
-Infinity
120
P2
0
44
100
-Infinity
144
P3
220
0
120
87.5
Infinity
P4
0
26
70
-Infinity
96
Constraint
Dual Value
Slack/Surplus
Original Val
Lower Bound
Upper Bound
Constraint 1
12
0
3200
1000
3333.333
Constraint 2
0
160
1000
840
Infinity
Constraint 3
0
40
1200
1160
Infinity
Constraint 4
-40
0
100
0
120
2. (a) Determine the optimal solution and optimal value and interpret their meanings.
(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.
3. (a) What are the ranges of optimali.
Economics 512 Homework IV (25 Points) Fall 2016 Do Pro.docxSALU18
Economics 512
Homework IV (25 Points)
Fall 2016
Do Problems 1, 2, 3, Below and 7-4, 7-10, 7-11, 9.3, 6-7, and Risk Analysis Questions
#3,5 and 8.
1. You make decorative stones for landscaping. A ton of coarse stones requires 2 hours
of crushing, 5 hours of sifting, and 8 hours of drying. A ton of fine stones requires 6
hours of crushing, 3 hours of sifting, and 2 hours of drying. The coarse stones sell for
$400 per ton. The fine stones sell for $800 per ton. In a work week your plant is capable
of 36 hours of crushing, 30 hours of sifting, and 40 hours of drying.
Use the graphical method first, to answer a. below. Then use your spreadsheet to verify
your answer and get the numbers you need for b. and c. For full credit for your graph,
draw the constraints and at least one iso-revenue line. Draw a circle or an arrow to
indicate the optimal point.
Determine:
a. How much of each kind of stones you should make to maximize your revenue.
b. How much revenue you'll make at the maximum.
c. How much it would be worth to you to get another hour of crushing time, sifting time,
or drying time.
2. You make three kinds of computers: Cheap, Good, and Deluxe. These sell for $1500,
$2000, and $2800. The Cheap model requires 3 hours for circuit board installation and 1
hour to fit the peripheral equipment. The Good model requires 1 hour for circuit boards
and 5 hours for peripherals. The deluxe model requires 3 hours for circuit boards and 2
hours for peripherals. You have 120 hours available for circuit board work and 60 hours
for fitting peripherals. Determine:
a. How much of each kind of computers you should make to maximize your revenue.
b. How much revenue you'll make at the maximum.
c. How much it would be worth to you to get another hour of circuit board assembly time
or peripheral fitting time.
This time you'll have to rely on your spreadsheet rather than the graph method. Why?
fr~cLJ c+f;"c-~ eD~-\- (Y\k{(IV'(-ZI~') 6\~+·~ e~.,-~
.......
Class A Class A Class A Class B Class B Beef Stocker
cotton milo wheat milo wheat cows steers
Units (acre) (acre) (acre) (acre) (acre) (head) (head)
Gross Margin $/UDlt S150 S100 $115 $85 $70 $205 $70 MAX
Class A land acre 1 1 1 0 0 0 0 LE
Class Bland acre 0 0 0 1 1 05 0 LE
Pasture acre 0 0 0 0 0 6 3 LE
Labor hour 4 3 2.5 3 25 6 1 LE
Rotation LimIt acre 1 0 0 0 0 0 0 LE
291
(c) lOx + 5y :::; 50
2y:::; 15
Jx:::; 9
x~O
v>O
(d) x + y:::; 40
2x + y:::; 60
Jx + Jy _ 60
x 0
y~O
7-2. Graph the fe~~sihle region defined h)' the following set ot Inequalities:
x + y.s; 40
2x + 4y :::; 100
3y .s; 60
x ~ 0
y~O
Using a graphic approach. determine thar poinr in the feasihle region (i.e.,
the values ot x and y) that minimizes e:\(h of the following ohtective
functions:
(<I) , x 3y
(b) z = 6x + 4y
7-3. Given the following linear progr,lm,
maximize n = 4Q .• + JQB
suhjeu to the followlIlg machine-time constraints:
Q" + 2QB .s;100
2Q" + ...
BUS 640 HOMEWORK Achievement Education--bus640homework.comclaric150
FOR MORE CLASSES VISIT
www.bus640homework.com
Week 1
Problem 1:
A generous university benefactor has agreed to donate a large amount of money for student scholarships. The money can be provided in one lump sum of $12 million in Year 0 (the current year), or in parts, in which $7 million can be provided at the end of Year 1, and another $7 million can be provided at the end of Year 2.
Describe your answer for each item below
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Normal Labour/ Stages of Labour/ Mechanism of LabourWasim Ak
Normal labor is also termed spontaneous labor, defined as the natural physiological process through which the fetus, placenta, and membranes are expelled from the uterus through the birth canal at term (37 to 42 weeks
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
RPMS TEMPLATE FOR SCHOOL YEAR 2023-2024 FOR TEACHER 1 TO TEACHER 3
Decision theory blockwood
1. Blockwood Inc. is a newly organized manufacturer of furniture products. The firm must decide what type
of truck to purchase for use in the company's operations. The truck is needed to pick up raw material
supplies, to make deliveries and to transport product samples to commercial exhibits during the coming
year. Three alternatives were identified by the firm:
(1) A small commercial import truck
(2) A standard size pick-up
(3) A large flatbed truck
It is expected that sales in the first year will fall in one of four categories:
(1) Low (0-200,000)
(2) Moderately low (200,000-400,000)
(3) Moderately high (400,000-600,000)
(4) High (above 600,000)
The payoff table for the firm would be:
Actions States of Nature
Truck Type Low Moderately Low Moderately High High
Import 20 10 15 25
Standard 15 25 12 20
Faltbed -20 -5 30 40
a) Find the appropriate decisions using
1) Laplace Criterion
2) Minimax Criterion (Assume loss payoff table)
3) Maximin Criterion
4) Savage Minimax Regret Criterion
5) Hurwicz Criterion (α = 0.6)
b) Suppose that the firm has assessed that probabilities for the 4 sales levels as:
P(1) = 0.20 P(3) = 0.30
P(2) = 0.35 P(4) = 0.15
What decision would be reached using Bayes' Rule?
c) Find the expected profit using Perfect Information Source (EPPI).
d) Find the expected value of perfect information (EVPI).
e) Suppose the firm acquires the services of a consulting firm, ABC Inc. ABC will conduct market study
that will result in one of 2 outcomes.
(1) O1 will be favorable indication of the market for the firm's products.
(2) O2 will be unfavorable indication of the market for the firm's products.
O1 and O2 are referred to as sample outcomes.
The following conditional probabilities were arrived at from considerable ABC experience, using
historical market research record in ABC's files and the statisticians' judgment.
P(Oj/SI)
S1 S2 S3 S4
O1 0.05 0.30 0.70 0.90
O2 0.95 0.70 0.30 0.10
Find the posterior probabilities, expected payoff with sample information, and expected value of
sample information
If ABC charges Php1000, find the expected net gain from sample information.
2. 1. Consider the following payoff (profit) matrix.
E1 E2 E3 E4 E5
A1 15 10 0 -6 17
A2 3 14 8 9 2
A3 1 5 14 20 -3
A4 7 19 10 2 0
No probabilities are known for the occurrence of the nature of states. Compare the solutions obtained
by each of the following criteria:
a. Laplace
b. Maximin
c. Savage Minimax Regret
d. Hurwicz (α = 0.7)
2. The daily demand for loaves of bread in a grocery store can assume one of the following values: 100,
120, or 130 loaves with probabilities 0.2, 0.3, and 0.5. The owner of the store is thus limiting her
alternatives to stocking one of the indicated three levels. If the stocks are more than she can sell in the
same day, she must dispose of the remaining loaves at a discount price of 55 cents/loaf. Assuming that
she pays 60 cents per loaf and sells it for $1.05, find the optimum stock level by using a decision tree
representation.
3. Consider problem no. 2, suppose that the owner wishes to consider her decision problem over a 2-day
period. Her alternatives for the second day are determined as follows. If the demand in day 1 is equal
to the amount stocked, she will continue to order the same quantity on the second day. Otherwise, if
the demand exceeds the amount stocked, she will have the options to order higher levels of stock on
the second day. Finally, if day 1's demand is less than the amount stocked, she will have the options to
order any of the lower levels of stock for the second day. Express the problem as a decision tree and
find the optimum using the cost data in problem no. 2.
4. Pizza King and Noble Greek are two competing restaurants. Each must determine simultaneously
whether to undertake small, medium, or large advertising campaigns. Pizza King believes that it is
equally likely that Noble Greek will undertake a small, medium or large advertising campaign. Given
the actions chosen by each restaurant, Pizza King’s profits are as shown in the table below.
Noble Greek Chooses
Pizza King Chooses Small Medium Large
Small $6000 $5000 $2000
Medium $5000 $6000 $1000
Large $9000 $6000 $0
Determine Pizza King’s choice for advertising campaign using the following criteria:
a) Laplace
b) Maximin
c) Minimax (assume given data are in terms of costs)
d) Savage Minimax Regret
e) Hurwicz (assume: α = 0.6)
f) Suppose that Pizza King has assessed that probabilities that Noble Greek will undertake the above
mentioned levels of advertising campaigns:
P(S) = 0.25
P(M) = 0.40
P(L) = 0.35
What decision would be reached using Bayes' Rule?
g) Find the expected profit using Perfect Information Source (EPPI).
3. h) Find the expected value of perfect information (EVPI).
i) Suppose Pizza King acquires the services of a consulting firm, ABC Inc. ABC will conduct
market study that will result in one of 2 outcomes.
(1) O1 will be favorable indication of the market for the firm's products.
(2) O2 will be unfavorable indication of the market for the firm's products.
O1 and O2 are referred to as sample outcomes.
The following conditional probabilities were arrived at from considerable ABC experience, using
historical market research record in ABC's files and the statisticians' judgment.
P(Oj/SI)
Market Study Outcome Small Medium Large
O1 0.05 0.30 0.70
O2 0.95 0.70 0.30
Find the posterior probabilities, expected payoff with sample information, and expected value of
sample information
If ABC charges $1,000, find the expected net gain from sample information.
5. Suppose that Pizza King and Noble Greek stop advertising but must determine the price they will
charge for each pizza sold. Pizza King believes that Noble Greek’s price is a random variable D
having the following mass function: P(D = $6) = 0.25, P(D = $8) = 0.50, P(D = $10) = 0.25. If Pizza
King charges a price p1 and Noble Greek charges a price p2, Pizza King will sell 100 + 25(p2 – p1)
pizzas. It costs Pizza King $4 to make a pizza. Pizza King is considering charging $5, $6, $7, $8, or
$9 for a pizza. Use each decision criterion to determine the price that Pizza King should charge.
4. Sequential Decision Making
The city of Metropolis is planning to construct a street that will run through the city perpendicular
to the main east-west street. The city planners have to make a choice between a modern, wide (4-
lane) street that would cost Php2M or a lesser-quality narrower street that would cost Php1M. We
shall denote these two alternatives as W1 and N1. After 4 years, depending on whether the traffic
on the street turns out to be light or heavy (LI or H1), the city will have the option of widening
the street. The probability of these traffic conditions are estimated by city planners and
economists as P(L1) = 0.25 and P(H1) = 0.75. If W1 is selected, maintenance expenses during
the first 4 years will be Php5,000 or Php75,000 depending on whether the traffic is light or heavy.
If N1 is selected, these costs are expected to be Php30,000 and Php150,000, respectively.
Suppose street W1 is built then at the end of 4 years, no further work is required. If heavy traffic
is experienced, either a minor or major repair must be made at costs of Php150,000 and
Php200,000, respectively. If street N1 is built then at the end of 4 years, if traffic has been light,
either a minor or major repair must be made at costs of Php50,000 and Php100,000, respectively.
If traffic has been heavy, major repair must be made at a cost of Php900,000. Traffic during the
next 6 years will be classified as light or heavy (L2 or H2). The probabilities of these two events,
conditional on the traffic condition in years 1-4, are given as follows:
P(L2/L1) = 0.75 P(L2/H1) = 0.10
P(H2/L1) = 0.25 P(H2/H1) = 0.90
Maintenance costs over years 5-10 will depend on which street was built in year 1, what type of
repair was made at the end of year 4, and the amount of traffic during years 5-10.
Street Repair Traffic Maintenance (Php)
Year 1 Years 5-10 Year 5-10
W1 None L2 200,000
H2 250,000
Minor L2 150,000
H2 175,000
Major L2 125,000
H2 100,000
N1 Minor L2 200,000
H2 250,000
Major L2 175,000
H2 150,000
a) Construct a decision tree for this problem.
b) Determine the optimal sequential strategy for the city of Metropolis