input: Write a python function to define and solve a linear programming cost minimization problem using PuLP.
  assert solve_linear_programming_problem() == {'x': 6.0, 'y': 2.0, 'total_cost': 34.0}
  assert solve_linear_programming_problem() == {'x': 6.0, 'y': 2.0, 'total_cost': 34.0}
  assert solve_linear_programming_problem() == {'x': 6.0, 'y': 2.0, 'total_cost': 34.0}
output: from pulp import LpProblem, LpVariable, LpMinimize, LpStatus, value
  
  def solve_linear_programming_problem():
      # Create the linear programming problem
      prob = LpProblem("CostMinimization", LpMinimize)
      
      # Define the decision variables
      x = LpVariable('x', lowBound=0)  # x >= 0
      y = LpVariable('y', lowBound=0)  # y >= 0
      
      # Define the objective function
      prob += 3*x + 4*y, "Total Cost"
      
      # Define the constraints
      prob += 2*x + y >= 12
      prob += -4*x + y <= 5
      prob += x >= 6
      
      # Solve the problem
      prob.solve()
      
      # Extract the results
      x_value = value(x)
      y_value = value(y)
      total_cost = value(prob.objective)
      
      return {'x': x_value, 'y': y_value, 'total_cost': total_cost}