The National Testing Agency has rescheduled the dates of JEE Main 2022. Earlier, it was supposed to start on June 20. According to the latest update, the exam will start on 23 June. Proper preparation and hard work are essential for cracking the JEE Main exam. Students should also achieve the speed to complete the problems within the given time. Therefore, practising previous years’ question papers and mock tests is highly recommended. It will also help the JEE aspirants to experience the real exam scenario.
Linear programming is a topic of great importance for the CBSE board exams. Hence, students are recommended to practice and learn linear programming problems so that they can score marks on this topic. If learnt properly, they can easily score full marks on this topic. Students can definitely expect questions from this topic for board exams. In this article, we will discuss linear programming, the corner point method, and linear equations.
What is Linear Programming?
Linear programming is about maximising or minimising a linear function subject to various constraints. A linear programming problem (LPP) deals with the optimisation problem of two linear variables. The function formed by using these two linear variables is termed an objective function. The problems from linear programming are not that complicated. So, students can easily score marks on this topic if learnt properly.
Following are some important terms that students need to learn in linear programming.
- Decision variables
- Non-negative constraints
- Optimisation problem
- Feasible region
- Infeasible region
- Optimal solution
The linear inequalities or equations on the variables of an LPP are known as constraints. A region that is common to all the constraints, including the non-negative constraints, is termed a feasible region. Linear programming has various applications in industrial engineering, in guiding quantitative decisions in business planning, in the social and physical sciences, etc. We use the corner point method to solve problems on linear programming.
Corner point method
In the corner point method, first, we have to find the feasible region of the LLP. Then we have to find the corner points either by substituting or by finding the solution of two equations of the lines intersecting at that point. Then, we have to find the objective function Z = ax+by at each corner point. Let M be the largest and m be the smallest values at these points. If the feasible region is bounded, M is the maximum value of Z, and m is the minimum value of Z.
A linear equation is an equation whose highest power of the variable is 1. From the exam point of view, linear equations are a topic of great importance. It is used in graph theory, least square approximation, determinants, etc. Students are advised to learn the previous years’ questions asked for the JEE Main exam so that they will be able to understand the difficulty level and pattern.
Learning resources for the JEE Main exam are available online on different websites. Students are advised to go through revision notes, important formula pdfs, chapter-wise question papers etc. Visit BYJU’S to learn more about linear programming and solutions from previous years’ questions on linear programming.