input: from typing import List
  
  def solve_linear_programming_problem(coefficients: List[float], constraints: List[List[float]], rhs: List[float], objective_type: str) -> List[float]:
      """ Solve a linear programming problem using the Simplex method. The input includes coefficients for the objective function, constraints (as a list of lists), right-hand side values for the constraints, and the type of objective ('max' or 'min').
      The output is a list of values for the decision variables that represent the optimal solution.
      >>> solve_linear_programming_problem([3, 2], [[1, 0], [0, 1], [1, 1]], [4, 6, 8], 'max')
      [4, 4]
      >>> solve_linear_programming_problem([2, 3, 4], [[1, 2, 3], [2, 1, 1], [1, 0, 0]], [10, 8, 4], 'min')
      [4, 0, 0]
      """
output:     from scipy.optimize import linprog
  
      num_vars = len(coefficients)
      num_constraints = len(constraints)
  
      # Convert the objective function to minimization form if it's a maximization problem
      if objective_type == 'max':
          coefficients = [-x for x in coefficients]
  
      # Convert constraints to standard form for linprog
      A = constraints
      b = rhs
  
      # Solve the linear programming problem using scipy's linprog
      result = linprog(coefficients, A_ub=A, b_ub=b, bounds=(0, None))
  
      # Extract the optimal values for the decision variables
      if result.success:
          return result.x.tolist()
      else:
          raise ValueError("No optimal solution found")