Linear Programming Problems Short Notes for GATE Exam

Linear Programming Problems Short Notes

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.


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 a1x1 + a2x2 + a3x3 +……….anxn


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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).


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


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


Minimize(Z) = 45x1 + 40x2 + 85x3     [Objective Function]

3x+ 4x+ 8x3 +  6x>= 800

2x1+ 2x+ 7x+ 5x>= 200     [Constraints]

6x1 + 4x2 + 7x3 + 4x>= 700

xxxx4 >= 0      [Variables]

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