input: 
  from typing import List
  
  
  def solve_linear_programming_problem_with_simplex(objective_function: List[float], constraints: List[List[float]], rhs: List[float], maximize: bool = True) -> List[float]:
      """Solve a linear programming problem using the Simplex method.
      
      The Simplex method is an algorithm for solving linear programming problems, 
      where the goal is to either maximize or minimize a linear objective function 
      subject to a set of constraints. The method iteratively moves from one 
      vertex of the feasible region to an adjacent vertex with a better objective 
      function value until the optimum is found.
      
      For example, to solve the following problem:
      Maximize Z = 3x + 4y
      Subject to:
          2x + y ≤ 4
          x + 2y ≤ 5
          x, y ≥ 0
      
      The function would be called as:
      >>> solve_linear_programming_problem_with_simplex([3, 4], [[2, 1], [1, 2]], [4, 5])
      [1.6666666666666667, 1.6666666666666665]
      
      This output indicates that the maximum value of the objective function (Z = 3x + 4y)
      occurs when x = 1.6666666666666667 and y = 1.6666666666666665 under the given constraints.
      """
  
output:     from scipy.optimize import linprog
  
      num_variables = len(objective_function)
      num_constraints = len(constraints)
  
      # Convert maximization problem to minimization
      if maximize:
          objective_function = [-x for x in objective_function]
  
      # Construct the linear programming problem
      c = objective_function
      A = constraints
      b = rhs
      x_bounds = [(0, None) for _ in range(num_variables)]
  
      # Solve the problem using the Simplex method
      result = linprog(c, A_ub=A, b_ub=b, bounds=x_bounds, method='simplex')
  
      if result.success:
          return result.x
      else:
          raise ValueError("The problem could not be solved.")