numpy lab(18/03/2024)

#Assignment: Write a Python Program to solve Linear Programming Problem using
#Simplex Method
import numpy as np

def simplex_method(A, b, c):
    m, n = A.shape
    # Create the initial tableau
    tableau = np.hstack([A, np.eye(m), b.reshape(-1, 1)])
    tableau = np.vstack([tableau, np.concatenate([c, np.zeros(m + 1)])])

    while True:
        # Find the pivot column
        pivot_col = np.argmin(tableau[-1, :-1])

        # If all elements in the last row are non-negative, optimal solution found
        if np.all(tableau[-1, :-1] >= 0):
            break

        # Find the pivot row
        ratios = tableau[:-1, -1] / tableau[:-1, pivot_col]
        pivot_row = np.argmin(ratios)

        # Perform pivot operation
        tableau[pivot_row, :] /= tableau[pivot_row, pivot_col]

        for i in range(m + 1):
            if i != pivot_row:
                tableau[i, :] -= tableau[i, pivot_col] * tableau[pivot_row, :]

    return tableau[-1, -1], tableau[-1, :-1]

A = np.array([[2, 1], [1, 2]])
b = np.array([4, 3])
c = np.array([-3, -5])

optimal_value, optimal_solution = simplex_method(A, b, c)

print("Optimal value:", optimal_value)
print("Optimal solution:", optimal_solution)

#Output
Optimal value: 8.333333333333334
Optimal solution: [0.         0.         0.33333333 2.33333333]