**Linear Programming Problems Short Notes**

Topics Discussed:

In this post, we try to understand the basics of Linear Programming Problems. We get to know the definition, the terms used, and then understanding the terms, their definition, and role in LPP.

**Introduction**

With **Linear Programming**, a technique, we approach towards optimization and come up with a better conclusion or results. Linearity means a mathematical expression comprising various variables in the form a_{1}x_{1 }+ a_{2}x_{2 }+ a_{3}x_{3 }+……….a_{n}x_{n}

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**Terms Used in LPP**

- Objective Function
- Constraints
- Variables

**Objective Function**

- A mathematical or logical expression consisting of decision variables. Function deciding the objective of the problem or task (optimization of a task).

**Variables**

- These are the individual factors contributing to attaining the goal.

**Constraints**

- Also called the influencing factors. Set of equations or inequalities consisting of the variables which affect or influence the objective function.

**Example**

Minimize(Z) = 45x_{1 }+ 40x_{2 }+ 85x_{3 }[Objective Function]

3x_{1 }+ 4x_{2 }+ 8x_{3 }+ 6x_{4 }>= 800

2x_{1}+ 2x_{2 }+ 7x_{3 }+ 5x_{4 }>= 200 [Constraints]

6x_{1 }+ 4x_{2 }+ 7x_{3 }+ 4x_{4 }>= 700

x_{1 }x_{2 }x_{3 }x_{4 } >= 0 [Variables]

**Read More: Techniques & Tools of Operation Research**