A problem is provided which is solved by using graphical and analytical method of linear programming method and then it is solved by using geometrical concept and algebraic concept of simplex method.
Linear programming
Application Of Linear Programming
Advantages Of L.P.
Limitation Of L.P.
Slack variables
Surplus variables
Artificial variables
Duality
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
Every linear programming problem has a dual problem. In certain situations, the dual problem has an interesting interpretation. In any case, the original ("primal") problem and the dual problem have the same extreme value
A problem is provided which is solved by using graphical and analytical method of linear programming method and then it is solved by using geometrical concept and algebraic concept of simplex method.
Linear programming
Application Of Linear Programming
Advantages Of L.P.
Limitation Of L.P.
Slack variables
Surplus variables
Artificial variables
Duality
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
Every linear programming problem has a dual problem. In certain situations, the dual problem has an interesting interpretation. In any case, the original ("primal") problem and the dual problem have the same extreme value
My talk about linear programming in NTU's APEX Club in NTU, Singapore in 2007. The club is for people who are keen on participating in ACM International Collegiate Programming Contests organized by IBM annually.
The term regression was originally employed by Francis Galton while describing the laws of inheritance. Galton believed that these laws caused population extremes to “regress
toward the mean.” By this he meant that children of individuals having extreme values of a certain characteristic would tend to have less extreme values of this characteristic
than their parent.
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Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
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2. Introduction
• One of the most important discoveries in the early
development of linear programming was the
concept of duality and its ramifications.
• discovery revealed that every linear programming
problem has associated with it another linear
programming problem called the dual. The
relationships between the dual problem and
the original problem (called the primal) prove
to be extremely useful in a variety of ways.
• We shall describe many valuable applications of
duality theory
3. Definition of the Dual
problem
• The dual problem is an LP defined systematically
from the primal (original) LP model.
• The two problems are so closely related
– the primal optimum solution automatically
provides the optimal solution to the dual.
• The primal problem represents
– a resource allocation case
• the dual problem represents
– a resource valuation problem.
• Duality help simplification of the simplex problem.
4. Rules for constructing the dual
problem
First modify the give PLP in the standard equation form
and use the following table.
Primal
Problem
Dual Problem
Objective Objective Constraints
Type
Variable sign
Maximization Minimization ≥ unrestricted
Minimization Maximization ≤ unrestricted
6. Example (1)
• Write the dual for the following primal problem:
• Maximize Z= 5x1 + 12x2 + 4x3
Subject to: x1+2x2+x3 ≤ 10
2x1- x2 + 3x3 = 8
x1,x2,x3 ≥ 0
What if you considered artificial variables to
change to standard form rather than equation
form???.....Try
7. Example (2)
• Write the dual for the following
primal problem
Maximize Z= 5x1 + 12x2 + 4x3
Subject to: x1+2x2+x3 ≤ 10
2x1- x2 + 3x3 = 8
x1,x2,x3 ≥ 0
9. Optimal Dual Solution
• The two methods for finding the
optimal value of the dual problems
• However, dual of the dual is itself the
primal, which means that the dual
solution can also be used to yield the
optimal primal solution automatically.