**CBSE Class 12 linear programming**helps to compute the maximum or minimum of the several quantities given. It could be finding minimum cost, maximum profit, or minimum resource usage, etc. This type of problem is also called an optimization problem. This article discusses the complete syllabus of linear programming to help students in the preparation.

**Introduction to Linear Programming**

- Linear programming problems and mathematical formulation
- A mathematical formulation of the problems
- Graphical method to solve linear programming problems

**Different kinds of Linear Programming Problems**

In this section, the following types of linear programming problems are included:

**Manufacturing problem**

Here a student maximizes the profit using minimum resource utilization.

**Diet Problem**

In this type of problem, a student must determine the various nutrients to include in the diet to reduce the manufacturing cost.

**Transportation problem**

In this case, a student may be required to determine the schedule to compute the affordable way to transport a product in minimum time.

**Terms Involved In Linear Programming Problem**

In Linear Programming, specific terms exist for the construction and solution of linear programming problems. Some of the important terms have been discussed below. A student needs to understand these terms and their practical application:

**Objective function:**

An objective linear function is characterized in the form of an equation as Z = ax + by. Here a and b are constants that need to be either maximized or minimized. The two variables, as x and y, are decision variables.

**Constraints:**

A constraint in a linear equation implies linear inequalities or restrictions imposed on the variables of a linear programming problem. One of the examples of these constraints is non-negative restrictions. It is seen in the form of a condition, x ≥ 0, y ≥ 0.

Examples of linear programming constraints are 4 x + y ≤ 80; x + y ≤ 40.

**Optimization problem:**

This kind of problem helps maximize and minimize any linear function subject to specific constraints, as shown by a group of linear dissimilarities.

**Feasible/Solution region:**

This is a common region shown by the given constraints that include non-negative constraints such as (x ≥ 0, y ≥ 0). It is called the feasible region for the problem. All the areas except feasible regions are known as the infeasible region.

A feasible region of any linear inequalities system is termed as bounded if it is enclosed in a circle. In all other cases, it is called unbounded. Unbounded region implies that the feasible region extends in any direction.

**Optimal solution:**

Any point present in the feasible region that provides the optimal value (minimum or maximum) of the objective linear function is termed as an optimal solution.

**About Index Numbers**

CBSE Class 12 index numbers and time-based data are other important concepts that help measure differences in relative variations at different times or places.

It is computed as the arithmetic mean to locate or represent a few specific data set values. An Index number assists in the computation of percentage variation in a phenomenon regarding a base parameter.

Index numbers are specific variables used for the computation of things that cannot be measured in absolute terms. In that case, specialized averages called index numbers come in handy. Students should study the three main types of index number quantity, value index number, and price.

Check all the details about: CBSE Class 12 Applied Mathematics

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