#Matric No= U22CS1088

This project implements the Simplex Algorithm in C++ to solve linear programming problems. The Simplex method is used to maximize or minimize a linear objective function subject to linear constraints.

• Supports standard form linear programming problems (maximization).
• Uses the tableau method for pivoting and iterating towards optimality.
• Detects unbounded solutions.
• Extracts the optimal values for the original variables.

The algorithm solves linear programming problems of the form:

Maximize: [ Z = c_1x_1 + c_2x_2 + ... + c_nx_n ]

1. Initialize the tableau by adding slack variables to convert inequalities to equalities.
2. Select the entering variable (most negative coefficient in the objective row).
3. Select the leaving variable using the minimum ratio test.
4. Pivot to update the tableau.
5. Repeat until all coefficients in the objective row are non-negative.
6. Extract the optimal solution and return the results.

To compile and run the program, use the following commands:

g++ simplex.cpp -o simplex
./simplex