Linear Programming Class 12 Project File

[Astryd Boschee]

HereI worked with a freshman-year teacher who was eager to try something different to open linear programming. As students wandered into class, they were given the initial problem. The Powerpoint slides are available for you to use.

One thing we would do differently here is letting students see the inequalities. We hid them, so as to maximize screen space. This would allow the teacher to turn the inequalities on or off, and emphasize where the colored dots reside.

One last thought here. The power of Desmos is evident for linear programming problems. The teachers I work with agree that having students graph these sorts of problems by hand is not only time-consuming, it is silly. By letting students experience the Desmos calculator, not only can we have real discussions of problems, we can tackle problems which may not be so graph-friendly.

This document provides an introduction to linear programming, including its definition, characteristics, formulation, and uses. Linear programming is a technique for determining an optimal plan that maximizes or minimizes an objective function subject to constraints. It involves expressing a problem mathematically and using linear algebra to determine the optimal values for the decision variables. Common applications of linear programming include production planning, portfolio optimization, and transportation scheduling.Read less

Linear programming projects portray real-life challenges and problem-solving through mathematical techniques. Methods of linear programming apply to a wide range of industrial contexts and problem scenarios. Modern-day businesses utilize LP models to plan the manufacturing process, schedule personnel, maximize office space, ensure timely delivery of goods, optimize shelf space, etc.

Linear programming is inherent in most statistics and machine learning models. Naturally, this special case of programming has emerged as a favorite among the teaching and learning communities of data science. But what is the reason behind taking a practical approach to understanding this topic?

A purely theoretical course can prove counterproductive in creating engaged learners. While students must know about the technicalities, it is equally essential to explore how the textbook knowledge applies in the real world. Recent reports have pointed out how overemphasis on straitjacket teaching methods is making pupils lose interest in Mathematics and Science.

Therefore, rather than learning the theories word for word, students must invest time working on real-life programming projects. Practically attempting multiple linear programming projects, they can also build their very own linear programming class 12 project pdf, which can definitely add to their portfolio in the future.

Here, we should note that these subjects focus on building logical thinking and reasoning capabilities, and hence, they contribute to the overall curriculum. So, how can we incorporate innovative tools in the classroom to improve the situation?

Activity-based learning offers a reliable solution for enhancing student engagement. When students take up group exercises or independent projects to solve actual issues, they can see academic concepts come to life. This assists them with knowledge retention and encourages them to discover new courses of action.

When educators use examples, they also introduce novices to the basics of management and decision-making. A standard realistic scenario of linear programming would include mentions of things like money, time, people, and space. The aim would be to employ the resources so that the organization can achieve minimum costs and maximum efficiency and profit. Familiarity with these fundamentals is vital in almost every career, be it engineering, the social sciences, or artistic pursuits.

Firstly, the simplification relationships should follow a straight line. Hence, the term linear. Secondly, all the values need to be subject to constraints, which may be in numerical or in terms or properties. And lastly, the solution has to optimize (i.e., maximize or minimize, depending on the problem) the quantity of a given variable.

LPP techniques are relevant for data scientists and programmers as well. You can get a significant headstart as a beginner if you know about different operations research procedures like the simplex method, graphical method, R, and OpenSolver. Overall, your task would involve reducing complexity and developing solutions capable of working under most conditions. Here are some topics to stimulate your creativity.

Once you have understood what linear programming is through linear programming class 12 project pdf and other practice methods, you will be able to tell the difference that it is not oddly similar to any programming language like Python or Java, rather it is a technique of mathematics to solve a kind of problem. The method is to find the derivatives or transform a matrix to solve the problem.

It calls a program and not a programming language because it is just an algorithm that helps solve problems, be it optimization, time management or space allocation. There are a hand full of day-to-day circumstances where linear programming can be implemented to make the results more efficient.

Once one is done knowing what they are, one can move on to learning one of the basic linear programming methods, the simplex method. It is a mainstream method of minimizing a linear function that has several variables and constraints to a less complex one.

After getting a grasp on the simplex method, one can move on to the dual simplex algorithm. The major difference between the simplex and dual simplex method is that in the simplex method, one has to start with a non-optimal yet feasible solution, while in the dual simplex method, one starts working with a solo optimal infeasible solution.

Once done with both, it is time to practice. Solvers in Python and R or any available programming language can be beneficial for practising while working with linear programming project pdf is another way to strengtne your skills.

Every business needs financial resources to get things started and sustain over time. Moreover, investors and credit providers usually ask for detailed analyses of profitability. And LPP can be immensely helpful in clearly explaining the viability of a business. This is a great optimization project example.

Let us suppose that you want to make a professional B-plan. First and foremost, you will have to define your problem using different variables, constraints, and the objective function. Then, you will solve the LPP using a suitable method, say a graph. Finally, you will evaluate your results and present your solution to the interested parties.

This problem relates to warehousing and the transfer of manufactured products. Here, you would need to minimize the cost of transporting goods with respect to the resources (motor vehicles and workforce) available in the storage facility and at every depot.

You can take up a project to showcase the feasibility of linear programming in improving supply chain modeling. Consider an industrial case that determines the best transportation schedule within the given limits and establishes an integrated supply chain.

You can employ sensitivity analysis to demonstrate how small changes in the model data can change the optimal solution. Furthermore, your project can add to the existing body of research while highlighting the major issues in supply chain modeling.

For delivery services companies (FedEx, Blue Dart, and such), identifying the shortest route to ship packages to their respective destinations forms a core task. This sort of distance optimization saves fuel and time and helps these logistics firms in improving customer experience.

Linear programming can help choose the specific path if a delivery person has to take six packages in a day from the warehouse (located at point X) to six different destinations (cities, namely L, M, N, O, P, and Q). You will need an objective function and linear inequalities subject to certain constraints.

The process of selecting this track can be termed as Operations Research. To solve the LP, you can use the simplex algorithm in a LINGO or LINDO package, depending on your convenience. And in this way, you will have a delivery model. Further, you can get creative and set the algorithm on an Excel worksheet.

As for the constraints, your study can include limits based on nutrition, cost, ecological aspects, or acceptability. You could design an integrated framework covering the domains of nutritional quality, economic feasibility, and environmental sustainability. A linear programming model is an ideal tool for this project as it allows you to satisfy multiple restrictions at once.

If you are just starting with LP modeling, you can try your hand at a chart with only two constraints (per gram nutrient content and unit costs). Your solution should minimize the cost of the diet and list the optimum quantity of different food items you can have in a day. The plan can be such that you eat at least 300 calories with 75 grams of protein, 65 grams of fat, and 300 grams of carbohydrates.

The details about the profit margins, market share, and fuel efficiency are available for all the models. Now, imagine a scenario where the top management wants to maximize the profits under these restrictions. It would be tricky to depict a strategy without simplifying the problem.

You can attempt a similar linear programming project based on the secondary data of any automaker. With this study, you can go a step further to analyze the implications of government policies on profitability. It is a unique way of looking at production planning problems that generally revolve around ERP data.

A study conducted by researchers at Landmark University, Nigeria, applied the optimization principle to allocate classroom space. Based on the data obtained from lecture halls and the committees of examination timetable management, the project sought to maximize the usage of the available classroom space. The result was a framework that reduced overcrowding and utilized the existing seating capacity in the best possible way.

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