input: 
  def solve_linear_programming_simplex_method():
      """
      Explain 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.
      """
      pass
  
output:     
      # Example problem: Maximize Z = 3x1 + 2x2 subject to constraints:
      # 1x1 + 0x2 <= 4
      # 0x1 + 1x2 <= 6
      # 3x1 + 2x2 <= 18
      # x1, x2 >= 0
  
      # Step 1: Define the problem
      c = [-3, -2]  # Coefficients of the objective function (maximize)
      A = [[1, 0], [0, 1], [3, 2]]  # Coefficients of the constraints
      b = [4, 6, 18]  # Right-hand side of the constraints
  
      # Step 2: Convert the problem into standard form
      # Introduce slack variables to convert inequalities to equalities
      num_variables = len(c)
      num_constraints = len(b)
      tableau = [[0] * (num_variables + num_constraints + 1) for _ in range(num_constraints + 1)]
  
      # Fill the tableau with coefficients
      for i in range(num_constraints):
          for j in range(num_variables):
              tableau[i + 1][j] = A[i][j]
          tableau[i + 1][num_variables + i] = 1  # Slack variable coefficients
          tableau[i + 1][-1] = b[i]  # Right-hand side of constraints
  
      # Fill the objective function row
      for j in range(num_variables):
          tableau[0][j] = c[j]
  
      # Step 3: Set up the starting solution in the tableau
      # The initial basic feasible solution is the slack variables
      basic_variables = list(range(num_variables, num_variables + num_constraints))
  
      # Step 4: Iteratively apply the Simplex algorithm
      while True:
          # Find the entering variable (most negative coefficient in the objective row)
          entering_var = min(range(num_variables + num_constraints), key=lambda x: tableau[0][x])
          if tableau[0][entering_var] >= 0:
              break  # No negative coefficients left, optimal solution found
  
          # Find the leaving variable (minimum ratio test)
          ratios = [tableau[i][-1] / tableau[i][entering_var] if tableau[i][entering_var] > 0 else float('inf') for i in range(1, num_constraints + 1)]
          leaving_var = min(range(num_constraints), key=lambda x: ratios[x]) + 1
  
          # Pivot on the entering and leaving variables
          pivot = tableau[leaving_var][entering_var]
          for j in range(num_variables + num_constraints + 1):
              tableau[leaving_var][j] /= pivot
  
          for i in range(num_constraints + 1):
              if i != leaving_var:
                  factor = tableau[i][entering_var]
                  for j in range(num_variables + num_constraints + 1):
                      tableau[i][j] -= factor * tableau[leaving_var][j]
  
          # Update the basic variables
          basic_variables[leaving_var - 1] = entering_var
  
      # Step 5: Determine the optimum solution
      solution = [0] * num_variables
      for i in range(num_constraints):
          if basic_variables[i] < num_variables:
              solution[basic_variables[i]] = tableau[i + 1][-1]
  
      return solution
  