This presentation about game theory particularly two players zero sum game for under graduate students in engineering program. It is part of operations research subject.
This presentation about game theory particularly two players zero sum game for under graduate students in engineering program. It is part of operations research subject.
These slides by the OECD Competition Division introduce the OECD background note presented during the discussion on "Price discrimination" held during the 126th meeting of the OECD Competition Committee on 30 November 2016. More papers and presentations on the topic can be found out at www.oecd.org/daf/competition/price-discrimination.htm
This presentation by Dennis CARLTON, Professor of Economics, University of Chicago Booth School of Business was made during the discussion on "Price discrimination" held during the 126th meeting of the OECD Competition Committee on 30 November 2016. More papers and presentations on the topic can be found out at www.oecd.org/daf/competition/price-discrimination.htm
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
Why linear programming is a very important topic?
• A lot of problems can be formulated as linear
programmes
• There exist efficient methods to solve them
• or at least give good approximations.
• Solve difficult problems: e.g. original example given
by the inventor of the theory, Dantzig. Best
assignment of 70 people to 70 tasks.
Assessing the Importance of Social Media and Social Networks to Rural College Students Seeking Employment highlights the use of Internet tools in finding jobs.
www.EdDansereau.com
Basic Break Even decision for managers. The break even calculation may be extend to help with outsource decisions.
Creative Commons allowed. All rights reserved Ed Dansereau @ 2016
How to set up a Graphical Method Linear Programming Problem - IntroductionEd Dansereau
How to set-up a simple linear programming problem using the Graphical Method. Excellent teaching tool before moving on to Simplex Method.. How to solve a linear programming problem.
Creative Commons allowed. All rights reserved by Ed Dansereau @ 2016
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
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!
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.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
2. Decision Variables
The two decision variables are the number of social media and newspaper ads.
Decision variables represent what management control. We can decide how
many of each to run.
X1 = Newspaper
X2 = Social Media
All other expressions (OF and Constraints are defined in terms of decision
variables).
3. Objective Function
Objective: Maximize Profit
Objective Function: How much profit from each of our decision variables.
$4 profit from Newspapers
$2 profit from Social Media
So
Zmax = 4X1 + 2X2
4. Constraints
Constraints are limitations, we can only dream of having unlimited resources
such as time and money.
For Budget Constraint
We have a maximum of 240 dollars, we could use 200 dollars but can not
spend 250. Our limitation is less than or equal to 240 dollars.
Each newspaper ad consumes $3 and each social media $1
Budget → 3X1 + 1X1 <= 240
6. Graph
Each constraint is Linear - a straight line. To graph we take advantage of the
straight lines and that the axis of any variable equals zero. The horizontal axis
is X1 and the Vertical is X2.
Budget
X1 → set X2 = 0, X1 + 2.5(0) <= 100, solve for X1, X1 = 100
X2 → set X1 = 0, 1(0) + 2.5X2 = 100, X2 = 40
Work Hours
8. Feasible Region
Feasible Region - the area limited by the
constraints.
Since our constraints are less than or equal to,
the feasible region is area below both lines.
Note that for most of the graph the binding
constraint is the blue line, after the point (76.9,
9.2) the binding constraint is the red line. All LP
problems assume greater than zero, so the axis
represents the other boundaries (you would not
do a project if your profits were negative).
Feasible Region
9. Extreme Points
Extreme Points are the points at the edges of
the feasible region. With two constraints there
are four extreme points, there can be more if
there are additional constraints.
Our extreme points are (the labels are arbitrary)
A: (0,0)
B: (0,40)
C: (76.9, 9.2)
Extreme Points
10. Optimal Solution
Any point within the feasible area is a solution
and will provide some measure of profit or at
least break-even
The Optimal Solution is the point that provides
the maximum profit given our constraints. In
Linear Programming it will always be one of the
extreme points regardless if the objective is to
maximizing profit or minimizing costs.
Put Coordinates of extreme points into
Objective Function to determine Maximum
Profit or Minimum Cost (Max profit in our
example).
Zmax = 4X1 + 2X2
Za (0,0) = 4(0)+ 2(0) = 0
Zb (0,40) = 4(0) +2(40) =40
Zc (76.9, 9.2) = 4(76.9) + 2(9.2) = 326Optimal Solution
11. Binding and Slack
A BINDING constraints limits the optimal
solution.
Slack is extra capacity.
For example the Budget constraint has slack up
until it intersects with the Work Hour constraint.
After that point, the Budget constraint is
binding.
12. Finding the intersection of two lines
There are three ways to determine the
intersection of two lines:
1. Estimate, take your best guess by looking
at graph, for our example I would guess
(77,10).
2. Simultaneous Solution
3. Mathematical Method
13. Simultaneous Solution
1. Write out the two linear lines, the constraint equations
2. Solve for one variable in terms of the other for first equation
3. Substitute solution into second equation, which will result a solution for
one variable
4. Solve for second variable
14. Simultaneous Solution
1. Write out two linear lines
a. Work Hours → X1 + 2.5X2 <= 100
b. Budget → 3X1 + X2 <= 240
2. Solve for one variable in terms of the other for first equation
a. X1 + 2.5X2 = 100, so X1 = 100 - 2.5X2
b. Solve for any variable in either equation. I choose Work Hours and the variable X1 because
the math was easy. With a coefficient of 1, (240-2.5X2)/1 = (240-2.5X2). You do not even
need a calculator for that!
15. Simultaneous Solution
3. Substitute solution into second equation, which will result a solution for one
variable
a. Budget → 3X1 + X2 <= 240
b. Work Hours → X1 = 100 - 2.5X2
c. Sub work hours into Budget → 3(100-2.5X2) + X2 = 240
i. 300 - 7.5X2 +x2 =240
ii. -6.5X2 = 240 - 300
16. Simultaneous Solution
4. Solve for second variable
X2 = 9.27
3X1 + X2 = 240 (either equation will work)
3X1 + 9.27 = 240
X1 = (240 - 9.27) / 3
X1 = 76.92, solution for second variable
17. Multiplication Method
In this method we try to eliminate one variable but multiplying by an inverse
(negative number).
1. Look at your two linear lines (constraints) and choose a variable to
eliminate. I look for a number that is easy to multiple.
2. Multiple the other equation by the inverse.
3. Add two equations together and solve for first variable.
4. Solve for second variable
18. Multiplication Method
1. Look at your two linear lines (constraints) and choose a variable to
eliminate
a. Budget → 3X1 + 1X2 <= 240
b. Hours → 1X1 + 2.5X2 <= 100
c. The X1 in budget is three times the X1 in hours, so I choose to multiple the Work Hours
constraint by inverse, or simply -3.
2. Multiple the other equation by the inverse
a. Hours → -3(1X1 +2.5X2 = 100),
19. Multiplication Method
3. Add two equations together and solve for first variable.
3X1 + 1X2 = 240
+ -3X1 - 7.5X2 = -300
= 0X1 - 6.5X2 = -60
X2 = (-60)/(-6.5)
X2 = 9.23 (Does this number look familiar?)
20. Multiplication Method
4. Solve for second variable
X2 = 9.23
Budget → 3X1 + 1X2 <= 240, you may choose either equation
3X1 + 9.23 = 240
X1 = (240 -9.23) / 3
X1 = 76.92
21. Finding the intersection of two lines
Both the Simultaneous Solution and Mathematical Method produce the same
solution for X1 and X2 (76.92, 9.23).
These coordinates are the point on the graph where the two lines intersect.
Yes, you need to learn both methods.
We will use the Mathematical Method in the next section.