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
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
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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.
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.
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.
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.
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.
2. Introduction
Operations Research is a systematic and analytical approach
to decision making and problem solving.
OR is a branch of applied mathematics that uses techniques
and statistics to arrive at optimal solutions to solve complex
problems.
It is typically concerned with determining the maximum
profit, sale, output, yield and efficiency and minimum
losses, risks, cost, and time.
4. Constructing a Model
Problem must be translated from
verbal, qualitative terms to logical and
quantitative terms.
A mathematical model is a collection
of functional relationships by which
allowable actions are delimited and
evaluated.
5. Solving a Mathematical Model
Many tools are available
Some lead to “optimal” solution
Others only evaluate candidates to
trial and error to find ”best” course of
action
6. Operations Research Models
Deterministic Model
Linear Programming
Network Optimization
Integer Programming
Non-Linear Programming
Stochastic/Probabilistic Model
• Discrete-Time Markov Chains
• Continuous-Time Markov Chains
• Queuing Theory
• Decision Analysis
7. Introduction to Linear Programming
Problem
A linear Programming model seeks to maximize or minimize a
linear function, subject to a set of linear constraints
A linear model consists of the following components:
◦ A set of decision variables
◦ An objective function
◦ A set of constraints
8. Process to formulate a LP problem
1. Identify the decision variables
2. Write the objective function
3. Mention the constraints
4. Explicitly state the non-negativity restrictions
For a problem to be a linear programming problem, the decision
variables, objective function and constraints all must be linear
functions.
9. Formulation of LPP
1. The decision variables (activities): These are activities for
which we want to determining a solution. These are usually
denoted by x1, x2, …, xn.
2. The objective function (goal): This is a function which is
expressed in terms of decision variables, and we want to
optimize (maximize or minimize) the function.
3. The constraints: These are limiting conditions on the use of
resources. The solution of LPP must satisfy all these
constraints.
10. Example 1
Consider a chocolate manufacturing company which produces only two types of chocolate –
A and B. Both the chocolates require Milk and Choco only.
To manufacture each unit of A and B, following quantities are required:
Each unit of A requires 1 unit of Milk and 3 units of Choco
Each unit of B requires 1 unit of Milk and 2 units of Choco
The company kitchen has a total of 5 units of Milk and 12 units of Choco. On each sale, the company
makes a profit of
Rs 6 and Rs 5 per unit sold of A and B respectively.
Now, the company wishes to maximize its profit. How many units of A and B should it produce
respectively
11. Example 1
Let, the total number of units of A and B be X and Y respectively.
Then,
Maximize Profit = Z = 6X +5Y
Subject to constraints:
X + Y ≤ 5
3X + 2Y ≤ 12
X ≥ 0 and Y ≥ 0
12. Example 2
A farmer has recently acquired a 110 hectares piece of land. He has decided to
grow Wheat and barley on that ;and. Due to the quality of the sun and the
region’s excellent climate. The entire production of wheat and barley can be sold.
He wants to know how to plant each variety in the 110 hectares given the costs,
net profit and labor requirements according to the data shown below. Given the
farmer has a budget of US$ 10,000 and an availability of 1200 man-days during
the planning horizon, find the optimal solution.
Variety Cost
(Price/Hec)
Net Profit
(Price/Hec)
Man-days/Hec
Wheat 100 50 10
Barley 200 120 30
13. Example 2
1. Decision variables:
The total are for growing Wheat = X (in
hectares)
The total are for growing Barley = Y (in
hectares)
2. Objective Function:
Max Z = 50X + 120Y
3. Constraints:
Subject to: 100X + 200Y ≤ 10,000
10X + 20Y ≤ 1200
X + Y ≤ 110
X ≥ 0 and Y ≥ 0