Optimizing Solutions-Linear Programming for Class 12
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Welcome to Linear Programming. Linear Programming is widely used in Mathematics and Statistics and Operation Research. In this page, I'll give you what exactly you need to know in Linear Programming for Class 12 Math.
You can access study tips, definitions and free video lessons here. In case you still need help, you can contact me for online tutoring. So, what exactly is Linear Programming?
Linear programming is a method for finding the optimum value of a linear function subject to constraints, which are linear equations or inequalities. The three classical types of Linear Programming problems are
i) Manufacturing problems
ii) Diet Problems
iii) Transportation problems
You need to know certain terms before you start
Objective function is the linear function which has to be maximised or minimised subject to constraints. You also have the non negativity constraints. The feasible region is the common region which is common to all the constraints.
We calculate the corner points of the feasible region. The feasible solution which maximises or minimises the objective function is called an optimal solution. An LPP may have more than one feasible solution.
To solve a problem using LPP, you need to first identify the objective function in terms of the variables x and y and then construct the constraints. Here, we'll be discussing only the graphical method to solve an LPP. You'll need to graph these constraints.
Next, you'll need to determine the feasible region. This may be bounded or unbounded. You consider the corner points of the feasible region.
Substitute the corner points in the objective function to find the optimal value. This is the Corner Point method. You also have the Transportation problems.
One example of this is when a factory has different godowns at different locations and it has to send its products to many places from these godowns. The transportation problem consists of transporting goods from different godowns to different places so that the transportation cost may be minimised.
This topic is simple, yet tricky. You have to analyze each problem thoroughly before starting. Writing the data in a tabular form helps create clarity.
All this and more will be discussed in my online classes. Learn how to solve multiple choice questions, conceptual based questions, assertion based questions, case study based questions and more.
Avail of regular graded tests. You can also access the youtube videos below for free resources.