Linear Programming (LP) is one of the most important topics in Optimization, Operations Research, Engineering, Data Science, and AI.
Yet, many students find it confusing — especially when they encounter constraints, corner points, feasible regions, and simplex tables.
In this article, I will explain Linear Programming Problems (LPP) using:
The Graphical Method (for intuition)
The Simplex Method (for larger problems)
👉 If you prefer video explanations, I also teach this step by step on my YouTube channel:
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What is a Linear Programming Problem (LPP)?
A Linear Programming Problem involves:
A linear objective function (to maximize or minimize)
A set of linear constraints
Non-negativity conditions
General form:
Maximize or Minimize
Graphical Method
The Graphical Method is used when there are two decision variables.
It helps students see what is happening instead of memorizing steps.
Key steps:
- Convert constraints into equations
- Plot them on a graph
- Identify the feasible region
- Determine the corner points
- Evaluate the objective function at each corner point
- Select the optimal value
Why the Graphical Method is important
- Builds intuition
- Helps you understand corner points
- Shows why the optimal solution occurs at extreme points
🎥 Watch the full Graphical Method tutorial here:
Graphical Method
Simplex Method
The Simplex Method is an iterative algorithm used to solve Linear Programming Problems with multiple constraints.
Main idea:
- Move from one corner point to another
- Improve the objective function at each step
- Stop when the optimal solution is reached
Key steps:
- Convert the problem into standard form
- Introduce slack variables
- Construct the initial simplex tableau
- Identify the pivot column and pivot row
- Perform row operations
- Interpret the final solution
🎥 Simplex Method (step-by-step) on YouTube:
Simplex Method
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