input: 
  def solve_linear_programming_problem_using_simplex_method():
      """
      This function explains the approach for solving a linear programming problem using the Simplex method in Python.
      The Simplex Method is an algorithm for solving a linear programming problem, which involves finding the maximum or minimum value of a linear function. 
      This method uses simultaneous equations to define a polytope that contains the solution to the linear programming problem. 
      It then finds the optimal solution in this polytope by iteratively making moves from a vertex to another in the polytope that gives an increase in the message value. 
      
      To solve a linear programming problem using the Simplex Method in Python, first, define the problem in terms of the decision variables, objective function, and constraints. 
      Next, convert the problem into standard form by introducing slack variables, if needed. 
      Then, create a tableau containing the coefficients of the decision variables and the right-hand sides of the constraints, and set up the starting solution in the tableau. 
      Now, iteratively use the Simplex algorithm to move from a vertex to the next until an optimum solution is reached. 
      Determine the optimum solution by inspecting the values in the tableau.
      """
  
  
output:     
      # Example problem:
      # Maximize Z = 3x1 + 2x2
      # Subject to:
      # 2x1 + x2 <= 18
      # 2x1 + 3x2 <= 42
      # 3x1 + x2 <= 24
      # x1, x2 >= 0
  
      # Step 1: Convert the problem into standard form by introducing slack variables
      # Maximize Z = 3x1 + 2x2 + 0s1 + 0s2 + 0s3
      # Subject to:
      # 2x1 + x2 + s1 = 18
      # 2x1 + 3x2 + s2 = 42
      # 3x1 + x2 + s3 = 24
      # x1, x2, s1, s2, s3 >= 0
  
      # Step 2: Create the initial tableau
      import numpy as np
  
      # Coefficients of the objective function
      c = np.array([3, 2, 0, 0, 0])
  
      # Coefficients of the constraints
      A = np.array([
          [2, 1, 1, 0, 0],
          [2, 3, 0, 1, 0],
          [3, 1, 0, 0, 1]
      ])
  
      # Right-hand side of the constraints
      b = np.array([18, 42, 24])
  
      # Step 3: Set up the initial solution in the tableau
      tableau = np.hstack((A, b.reshape(-1, 1)))
      tableau = np.vstack((tableau, np.append(c, 0)))
  
      # Step 4: Iteratively apply the Simplex algorithm
      def simplex_method(tableau):
          while True:
              # Find the pivot column (most negative coefficient in the objective row)
              pivot_col = np.argmin(tableau[-1, :-1])
  
              # If there are no negative coefficients, we have reached the optimal solution
              if tableau[-1, pivot_col] >= 0:
                  break
  
              # Find the pivot row (minimum ratio test)
              ratios = tableau[:-1, -1] / tableau[:-1, pivot_col]
              ratios[ratios <= 0] = np.inf  # Ignore negative and zero ratios
              pivot_row = np.argmin(ratios)
  
              # Perform the pivot operation
              tableau[pivot_row] /= tableau[pivot_row, pivot_col]
              for i in range(len(tableau)):
                  if i != pivot_row:
                      tableau[i] -= tableau[i, pivot_col] * tableau[pivot_row]
  
          return tableau
  
      # Step 5: Determine the optimum solution
      final_tableau = simplex_method(tableau)
      optimal_solution = final_tableau[-1, -1]
      decision_variables = final_tableau[:-1, -1]
  
      return optimal_solution, decision_variables
  