input: def solve_linear_programming_problem_using_simplex_method(problem_description: str) -> str:
      """
      Explain the approach for solving a linear programming problem using the Simplex method in Python.
      >>> solve_linear_programming_problem_using_simplex_method('Find the maximum value of 3x + 4y subject to x + y <= 5, x >= 0, y >= 0.')
      '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:     import re
  
      # Extract the objective function and constraints from the problem description
      objective_match = re.search(r'Find the (maximum|minimum) value of (.*) subject to', problem_description)
      if not objective_match:
          return "Invalid problem description format."
      
      objective_type = objective_match.group(1)
      objective_function = objective_match.group(2)
      
      constraints_match = re.findall(r'([xy]\s*[<>=]+\s*\d+)', problem_description)
      constraints = [constraint.strip() for constraint in constraints_match]
  
      # Convert the objective function and constraints into a standard form
      objective_coefficients = re.findall(r'([+-]?\d*[xy])', objective_function)
      objective_coefficients = [coef.replace(' ', '') for coef in objective_coefficients]
  
      # Create the initial tableau
      tableau = []
      for constraint in constraints:
          constraint_coefficients = re.findall(r'([+-]?\d*[xy])', constraint)
          constraint_coefficients = [coef.replace(' ', '') for coef in constraint_coefficients]
          rhs = re.search(r'([<>=]+\s*(\d+))', constraint).group(2)
          tableau.append(constraint_coefficients + [rhs])
  
      # Add slack variables to convert inequalities to equalities
      num_constraints = len(constraints)
      for i in range(num_constraints):
          tableau[i].extend([1 if j == i else 0 for j in range(num_constraints)])
  
      # Add the objective function row to the tableau
      tableau.append([-float(coef[:-1]) if coef[-1] == 'x' else 0 for coef in objective_coefficients] + [0] * (num_constraints + 1))
  
      # Simplex algorithm
      while any(coef < 0 for coef in tableau[-1][:-1]):
          # Find the pivot column
          pivot_col = tableau[-1].index(min(tableau[-1][:-1]))
          
          # Find the pivot row
          ratios = [tableau[i][-1] / tableau[i][pivot_col] if tableau[i][pivot_col] > 0 else float('inf') for i in range(num_constraints)]
          pivot_row = ratios.index(min(ratios))
          
          # Normalize the pivot row
          pivot_value = tableau[pivot_row][pivot_col]
          tableau[pivot_row] = [val / pivot_value for val in tableau[pivot_row]]
          
          # Update other rows
          for i in range(len(tableau)):
              if i != pivot_row:
                  factor = tableau[i][pivot_col]
                  tableau[i] = [val - factor * tableau[pivot_row][j] for j, val in enumerate(tableau[i])]
  
      # Extract the solution
      solution = {}
      for i, coef in enumerate(tableau[-1][:-1]):
          if coef == 0:
              solution[f'x{i+1}'] = tableau[i][-1]
  
      return f"The optimal solution is {solution} with a {objective_type} value of {tableau[-1][-1]}."