nono# Simplex Algorithm Solver

A C++ implementation of the Simplex method for solving Linear Programming problems. This program efficiently finds the optimal solution to a given set of linear constraints and an objective function using the tableau method.

Features

✅ Implements the Simplex Algorithm for Linear Programming ✅ Iterative approach to ensure optimality ✅ Detects unbounded solutions ✅ User-friendly output with formatted tableau representation ✅ Structured and modular code for easy understanding and modification

Installation & Usage

1️⃣ Compile the Program

Ensure you have a C++ compiler installed (e.g., g++ for GCC).

g++ simplex_solver.cpp -o simplex_solver

2️⃣ Run the Program

./simplex_solver

Project Structure

📁 Simplex Solver Project
│── simplex_solver.cpp   # Main program implementing the Simplex method
│── README.md            # Project documentation

How It Works

1️⃣ Initial Tableau Creation: Represents the LP problem as a tableau. 2️⃣ Pivot Column Selection: Identifies the most negative coefficient in the objective function row. 3️⃣ Pivot Row Selection: Uses the minimum ratio test to determine the leaving variable. 4️⃣ Pivoting Operation: Converts the pivot element to 1 and other elements in the column to 0. 5️⃣ Iteration Until Optimality: The algorithm repeats until all coefficients in the last row are non-negative.

Example Output

Initial Tableau:
     2.00     3.00     1.00     0.00     0.00   100.00 
     4.00     1.00     0.00     1.00     0.00    80.00 
     3.00     2.00     0.00     0.00     1.00    60.00 
    -3.00    -5.00     0.00     0.00     0.00     0.00 

Pivot Column: 1
Pivot Row: 1
Updated Tableau:
...

Optimal Solution:
Z = 166.67

Possible Future Improvements

Allow user input for constraints and objective function
Enhance output format with better visualization
Implement Graphical Method for 2-variable problems

Contributors

This project was developed as part of an assignment given by Mr. Rupert (GitHub: @Waboke).

Team Members:

📌 U22CS1039
📌 U22CS1037 📌 U22CS1040
📌 U22CS1041
📌 U22CS1080
📌 U22CS1044
📌 U22CS1045
📌 U22CS1046
📌 U22CS1115
📌 U19CS1106

License

This project is open-source and available under the MIT License.

Contractor-x/Simplex-Algorithm-C-

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